Updated on 2024/05/19

写真a

 
KOJIMA Hideo
 
Organization
Academic Assembly Institute of Science and Technology Fundamental Sciences Professor
Graduate School of Science and Technology Electrical and Information Engineering Professor
Faculty of Science Department of Science Professor
Title
Professor
External link

Degree

  • 博士(理学) ( 1999.3   大阪大学 )

Research Interests

  • Normal algebraic surfaces

  • Open algebraic surfaces

  • Logarithmic Kodaira dimension

  • Affine algebraic surfaces

Research Areas

  • Natural Science / Algebra  / Algebraic Geometry

Research History (researchmap)

  • Niigata University   Professor

    2013.4

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  • Niigata University   Professor

    2010.9 - 2013.3

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  • Niigata University   Associate Professor

    2004.4 - 2010.8

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  • Niigata University   Lecturer

    2002.4 - 2004.3

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  • Naruto University of Education   College of Education   Research Assistant

    2000.11 - 2002.3

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  • Osaka University

    2000.4 - 2000.11

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  • Osaka University

    1999.4 - 2000.3

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  • Osaka University

    1997.4 - 1999.3

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Research History

  • Niigata University   Faculty of Science Department of Science   Professor

    2017.4

  • Niigata University   Graduate School of Science and Technology Electrical and Information Engineering   Professor

    2013.4

  • Niigata University   Graduate School of Science and Technology Electrical and Information Engineering   Professor

    2013.4

  • Niigata University   Faculty of Science Department of Mathematics   Professor

    2013.4 - 2017.3

  • Niigata University   Faculty of Engineering Department of Information Engineering   Professor

    2010.9 - 2013.3

  • Niigata University   Faculty of Engineering Department of Information Engineering   Associate Professor

    2004.4 - 2010.8

  • Niigata University   Faculty of Engineering   Lecturer

    2002.4 - 2004.3

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Education

  • Osaka University   大学院理学研究課博士後期課程   数学専攻

    1997.4 - 1999.3

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  • Osaka University   Graduate School of Science   数学専攻

    1995.4 - 1997.3

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  • Niigata University   Faculty of Science   Department of Mathematics

    1991.4 - 1995.3

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Professional Memberships

 

Papers

  • Rings of nilpotent elements of monomial derivations on polynomial rings Reviewed

    Kyohei Hattori, Hideo Kojima

    Communications in Algebra   52 ( 7 )   2998 - 3009   2024.2

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    Authorship:Last author, Corresponding author   Publishing type:Research paper (scientific journal)   Publisher:Informa UK Limited  

    DOI: 10.1080/00927872.2024.2312459

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  • Smooth affine G_m-surfaces with finite Picard groups and trivial units Reviewed

    Hideo Kojima

    Tokyo Journal of Mathematics   46 ( 1 )   93 - 109   2023.6

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  • Normal log canonical del Pezzo surfaces of rank one and type (IIb) Reviewed

    Hideo Kojima, Takeshi Takahashi

    Saitama Mathematical Journal   34   47 - 72   2022.2

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  • Some results on open algebraic surfaces of logarithmic Kodaira dimension zero Reviewed

    Hideo Kojima

    Journal of Algebra   547   238 - 261   2020.4

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  • Singularities of Normal Log Canonical del Pezzo Surfaces of Rank One Invited Reviewed

    Hideo Kojima

    Polynomial rings and affine algebraic geometry, Springer Proc. Math. Stat.   319   199 - 208   2020

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    Authorship:Lead author   Language:English   Publishing type:Research paper (international conference proceedings)  

    DOI: 10.1007/978-3-030-42136-6_8

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  • Closed polynomials and their applications for computations of kernels of monomial derivations Reviewed

    Chiaki Kitazawa, Hideo Kojima, Takanori Nagamine

    JOURNAL OF ALGEBRA   533   266 - 282   2019.9

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    In this paper, we give some results on closed polynomials and factorially closed polynomials in n variables which are generalizations of results in [7], [12] and [13]. In particular, we give a characterization of factorially closed polynomials in n variables over an algebraically closed field of any characteristic. Furthermore, as an application of results on closed polynomials, we determine kernels of non-zero monomial derivations on the polynomial ring in two variables over a UFD. Finally, by using this result and the argument in [16, 5], for a field k, we determine the non-zero monomial derivations D on k[x, y] such that the quotient field of the kernel of D is not equal to the kernel of D in k(x, y). (C) 2019 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jalgebra.2019.06.001

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  • Log del Pezzo surfaces of rank one containing the affine plane Reviewed

    Hideo Kojima, Takeshi Takahashi

    Nihonkai Mathematical Journal   29 ( 2 )   77 - 130   2018.12

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  • Rational unicuspidal curves on Q-homology projective planes whose complements have logarithmic Kodaira dimension -∞ Reviewed

    Hideo Kojima

    Nihonkai Mathematical Journal   29 ( 1 )   29 - 43   2018.6

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  • Irrational open surfaces of non-negative logarithmic Kodaira dimension Reviewed

    Kojima Hideo

    ALGEBRAIC VARIETIES AND AUTOMORPHISM GROUPS   75   189 - 206   2017

  • NOTES ON THE KERNELS OF LOCALLY FINITE HIGHER DERIVATIONS IN POLYNOMIAL RINGS Reviewed

    Hideo Kojima

    COMMUNICATIONS IN ALGEBRA   44 ( 5 )   1924 - 1930   2016

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:TAYLOR & FRANCIS INC  

    Let A = k([3]) be the polynomial ring in three variables over a field k, and let D be a nontrivial locally finite iterative higher derivation on A. Let A(D) denote the kernel of D. In this note, we prove that, if char k > 0 and ML(A(D)) not equal A(D), then A(D) congruent to k([2]). As a consequence of this result, we give another proof of the cancellation theorem for k([2]) over any field k of positive characteristic.

    DOI: 10.1080/00927872.2015.1027387

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  • Closed polynomials in polynomial rings over integral domains Reviewed

    Hideo Kojima, Takanori Nagamine

    JOURNAL OF PURE AND APPLIED ALGEBRA   219 ( 12 )   5493 - 5499   2015.12

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ELSEVIER SCIENCE BV  

    Let f be a non-constant polynomial in the polynomial ring R-[n] in n variables over an integral domain R such that Q(R)[f] boolean AND R-[n] = R[f]. We give necessary and sufficient conditions for f to be closed in R-[n]. (C) 2015 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.jpaa.2015.05.028

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  • CLOSED POLYNOMIALS IN POLYNOMIAL RINGS OVER UNIQUE FACTORIZATION DOMAINS Reviewed

    Masaya Kato, Hideo Kojima

    COMMUNICATIONS IN ALGEBRA   43 ( 5 )   1935 - 1938   2015

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    Let R be a UFD, and let M(R, n) be the set of all subalgebras of the form R[f], where fR[x(1),..., x(n)]\R. For a polynomial fR[x(1),..., x(n)]\R, we prove that R[f] is a maximal element of M(R, n) if and only if it is integrally closed in R[x(1),..., x(n)] and Q(R)[f] R[x(1),..., x(n)]=R[f]. Moreover, we prove that, in the case where the characteristic of R equals zero, R[f] is a maximal element of M(R, n) if and only if there exists an R-derivation on R[x(1),..., x(n)] whose kernel equals R[f].

    DOI: 10.1080/00927872.2013.879876

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  • Normal log canonical del Pezzo surfaces of rank one with unique singular points Reviewed

    Hideo Kojima

    Nihonkai Mathematical Journal   25 ( 2 )   105 - 118   2014.12

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  • LOCALLY FINITE ITERATIVE HIGHER DERIVATIONS ON k[x, y] Reviewed

    Hideo Kojima

    COLLOQUIUM MATHEMATICUM   137 ( 2 )   215 - 220   2014

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ARS POLONA-RUCH  

    We give a new proof of Miyanishi's theorem on the classification of the additive group scheme actions on the affine plane.

    DOI: 10.4064/cm137-2-6

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  • Supplement to "Normal del Pezzo surfaces of rank one with log canonical singularities" by H. Kojima and T. Takahashi [J. Algebra 360 (2012) 53-70] Reviewed

    Hideo Kojima

    JOURNAL OF ALGEBRA   377   312 - 316   2013.3

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    Kojima and Takahashi (2012) [5] proved that every normal del Pezzo surface of rank one with only rational log canonical singular points has at most five singular points. In this paper, we determine such surfaces with five singular points. (C) 2012 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jalgebra.2012.11.028

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  • Open algebraic surfaces of logarithmic Kodaira dimension one Reviewed

    Hideo Kojima

    AFFINE ALGEBRAIC GEOMETRY   135 - 159   2013

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    We give a structure theorem for open algebraic surfaces of logarithmic Kodaira dimension one in arbitrary characteristic. Moreover, by using the structure theorem, we give some results on logarithmic plurigenera of normal affine surfaces of logarithmic Kodaira dimension one.

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  • Normal del Pezzo surfaces of rank one with log canonical singularities Reviewed

    Hideo Kojima, Takeshi Takahashi

    JOURNAL OF ALGEBRA   360   53 - 70   2012.6

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    We study normal del Pezzo surfaces of rank one with only log canonical singularities. Under some additional assumptions, we classify such surfaces. Moreover, we prove that every normal del Pezzo surface of rank one with only rational log canonical singularities has at most five singular points. (c) 2012 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jalgebra.2012.02.026

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  • Normal affine surfaces with non-positive Euler characteristic Reviewed

    Hideo Kojima

    Saitama Mathematical Journal   29   65 - 77   2012

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  • OPEN ALGEBRAIC SURFACES WITH (kappa)over-bar = (p)over-bar(g)=0 AND (P)over-bar(2) > 0 Reviewed

    Hideo Kojima

    OSAKA JOURNAL OF MATHEMATICS   48 ( 4 )   1063 - 1084   2011.12

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:OSAKA JOURNAL OF MATHEMATICS  

    Let S be a smooth open rational surface with (kappa) over bar (S) = (p) over bar (g)(S) = 0 and (P) over bar (2)(S) > 0. We construct a certain minimal model of S. which is called a strongly minimal model of S in [15], and determine the strongly minimal model in the case where S has non-contractible boundary at infinity. As an application, we classify the log affine surfaces with (kappa) over bar = (p) over bar (g) = 0 and (P) over bar (2) > 0 under the minimality condition.

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  • On the kernels of some higher derivations in polynomial rings Reviewed

    Hideo Kojima

    JOURNAL OF PURE AND APPLIED ALGEBRA   215 ( 10 )   2512 - 2514   2011.10

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    Let A = R[x(1), .... , x(n)] be the polynomial ring in n variables over an integral domain R with unit, let D be a rational higher R-derivation on A and let (D) over bar be the extension of D to the quotient field of A. We prove that, if the transcendental degree of the kernel of D over R is not less than n - 1, then the quotient field of the kernel of D equals the kernel of (D) over bar. Moreover, when n = 2, we give a necessary and sufficient condition for an R-subalgebra of A to be expressed as the kernel of a rational higher R-derivation on A. (C) 2011 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.jpaa.2011.02.010

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  • KERNELS OF HIGHER DERIVATIONS IN R[x, y] Reviewed

    Hideo Kojima, Norihiro Wada

    COMMUNICATIONS IN ALGEBRA   39 ( 5 )   1577 - 1582   2011

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    Let R be an HCF-ring and R[x, y] the polynomial ring in two variables over R. In this article, we prove that the kernel of any nontrivial higher R-derivation on R[x, y] has the form R[h] for some h is an element of R[x, y].

    DOI: 10.1080/00927871003660200

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  • AN ALGORITHM FOR COMPUTING THE KERNEL OF A LOCALLY FINITE HIGHER DERIVATION UP TO A CERTAIN DEGREE Reviewed

    Yuki Ito, Hideo Kojima

    COLLOQUIUM MATHEMATICUM   122 ( 1 )   21 - 31   2011

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    This paper gives an algorithm for computing the kernel of a locally finite higher derivation on the polynomial ring k[x(1), ..., x(n)] up to a given bound.

    DOI: 10.4064/cm122-1-3

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  • Notes on minimal compactifications of the affine plane Reviewed

    Hideo Kojima, Takeshi Takahashi

    ANNALI DI MATEMATICA PURA ED APPLICATA   188 ( 1 )   153 - 169   2009.1

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER HEIDELBERG  

    In this paper, we consider the minimal compactifications X of the complex affine plane with at most log canonical singular points. We classify the surfaces X in the case X has at least one non-log terminal singular point.

    DOI: 10.1007/s10231-008-0069-2

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  • Remarks on numerically positive line bundles on normal surfaces Reviewed

    Erika Emura, Hideo Kojima

    Contributions to Algebra and Geometry   39 ( 5 )   1577 - 1582   2009

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  • Affine lines on Q-homology planes with logarithmic kodaira dimension -infinity (vol 13, pg 1, 2008) Reviewed

    Takashi Kishimoto, Hideo Kojima

    TRANSFORMATION GROUPS   13 ( 1 )   211 - 213   2008.3

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    Language:English   Publisher:BIRKHAUSER BOSTON INC  

    DOI: 10.1007/s00031-008-9007-z

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  • Correction to: "Affine lines on Q -homology planes with logarithmic Kodaira dimension −∞ '' [Transform. Groups 11 (2006), no. 4, 659–672] Reviewed

    Hideo Kojima, Takashi Kishimoto

    Transformation Groups   13 ( 1 )   211 - 213   2008

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  • Logarithmic plurigenera of smooth affine surfaces with finite Picard groups Reviewed

    Hideo Kojima

    COMMENTARII MATHEMATICI HELVETICI   83 ( 3 )   547 - 571   2008

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:EUROPEAN MATHEMATICAL SOC  

    Let S be a smooth complex affine surface with finite Picard group. We prove that if (kappa) over bar (S) = 1 (resp. (kappa) over bar (S) = 2), then (P) over bar (2)(S) > 0 (resp. (P) over bar (6)(S) > 0) and determine the surface S when (kappa) over bar (S) >= 0 and (P) over bar (6)(S) = 0. Moreover, we prove that if Pic(S) = (0), Gamma(S, O-S)* = C* and (P) over bar (2)(S) = 0, then S congruent to C-2.

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  • On the logarithmic bigenera of some affine surfaces Reviewed

    Hideo Kojima

    Affine algebraic geometry, Osaka Univ. Press, Osaka, 2007   257 - 273   2007

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  • Affine lines on ℚ-homology planes with logarithmic Kodaira dimension -∞ Reviewed

    Takashi Kishimoto, Hideo Kojima

    Transformation Groups   11 ( 4 )   659 - 672   2006.12

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    In the present paper we study a topologically contractible irreducible algebraic curve C on a ℚ-homology plane S with κ̄ (S) = -∞ We determine such a pair (SC) when κ̄ (S\\C) ≥ 0 and C is smooth. Moreover we prove that if C is not smooth then C has exactly one singular point and theMakar-Limanov invariant of S is trivial. © Birkhauser Boston 2006.

    DOI: 10.1007/s00031-005-1121-6

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  • Reducible curves on rational surfaces Reviewed

    Hideo Kojima, Takeshi Takahashi

    Tokyo Journal of Mathematics   29 ( 2 )   301 - 317   2006

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    DOI: 10.3836/tjm/1170348169

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  • On the logarithmic plurigenera of complements of plane curves Reviewed

    H Kojima

    MATHEMATISCHE ANNALEN   332 ( 1 )   1 - 15   2005.5

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    Let B be a ( not necessarily irreducible) plane curve in P-2. In the present article, we prove that.( P-2 - B) >= 0 if and only if (P) over bar (6)( P-2 - B) > 0. Moreover, we determine the curve B when.( P-2 - B) = 0 and (P) over bar (4)( P-2 - B) = 0.

    DOI: 10.1007/s00208-004-0607-1

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  • Notes on minimal normal compactifications of C 2 /G Reviewed

    Hideo Kojima

    Nihonkai Mathematical Journal   15 ( 2 )   127 - 136   2004.12

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Niigata University  

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  • Rank one log del Pezzo surfaces of index two Reviewed

    H Kojima

    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY   43 ( 1 )   101 - 123   2003.6

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    Let S be a rank one log del Pezzo surface of index two and So the smooth part of S. In this paper we determine the singularity type of S, in a way different from Alekseev and Nikulin [1]. Moreover, we calculate the fundamental group of So and prove that S contains the affine plane as a Zariski open subset if and only if pi(1) (S-0) = (1).

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  • A note on Sakai's theorem concerning polarized normal surfaces Reviewed

    H Kojima

    ARCHIV DER MATHEMATIK   80 ( 3 )   239 - 244   2003.3

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    Working over an algebraically closed field of arbitrary characteristic, we classify. polarized normal surfaces in terms of logarithmic Kodaira dimension.

    DOI: 10.1007/s00013-003-4598-z

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  • Algebraic compactifications of some affine surfaces Reviewed

    H Kojima

    ALGEBRA COLLOQUIUM   9 ( 4 )   417 - 425   2002.12

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    We give a list of all minimal normal algebraic compactifications of A(k)(1) X A((r))(1), where A((r))(1) - {r points} (r greater than or equal to 1), by using a purely algebraic k method. 2000 Mathematics Subject Classification: primary 14J26, secondary 14DO6.

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  • Structure of affine surfaces P-2-B with (kappa)over-bar <= 1 Reviewed

    H Kojima

    JOURNAL OF ALGEBRA   253 ( 1 )   100 - 111   2002.7

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    DOI: 10.1016/S0021-8693(02)00060-1

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  • Minimal singular compactifications of the affine plane Reviewed

    Hideo Kojima

    Nihonkai Mathematical Journal   12 ( 2 )   165 - 195   2001.12

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Niigata University  

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  • On normal surfaces with strictly nef anticanonical divisors Reviewed

    H Kojima

    ARCHIV DER MATHEMATIK   77 ( 6 )   517 - 521   2001.12

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  • Open surfaces of logarithmic Kodaira dimension zero in arbitrary characteristic Reviewed

    H Kojima

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   53 ( 4 )   933 - 955   2001.10

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:MATH SOC JAPAN  

    in this article we study nonsingular rational open surfaces of logarithmic Kodaira dimension zero with connected boundaries at infinity defined over an algebraically closed field of arbitrary characteristic. We establish a classification theory of nonsingular affine surfaces of logarithmic Kodaira dimension zero and give a characterization of A(+)(1) x A(*)(1) in arbitrary characteristic.

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  • Complements of plane curves with logarithmic Kodaira dimension zero Reviewed

    H Kojima

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   52 ( 4 )   793 - 806   2000.10

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    We prove that logarithmic geometric genus of a complement of plane curve with logarithmic Kodaira dimension zero is equal to one.

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  • On Veys' conjecture Reviewed

    H Kojima

    INDAGATIONES MATHEMATICAE-NEW SERIES   10 ( 4 )   537 - 538   1999.12

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    We show that W. Veys' conjecture which was proved by A.J. de Jong and J.H.M. Steenbrink easily follows from S. Iitaka's virtual singularity theorem and the log Miyaoka-Yau inequality.

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  • Open rational surfaces with logarithmic Kodaira dimension zero Reviewed

    H Kojima

    INTERNATIONAL JOURNAL OF MATHEMATICS   10 ( 5 )   619 - 642   1999.8

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:WORLD SCIENTIFIC PUBL CO PTE LTD  

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  • Logarithmic del Pezzo surfaces of rank one with unique singular points Reviewed

    Hideo Kojima

    Japanese Journal of Mathematics   25 ( 2 )   343 - 375   1999

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    DOI: 10.4099/math1924.25.343

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  • Almost minimal embeddings of quotient singular points into rational surfaces Reviewed

    H Kojima

    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY   38 ( 1 )   77 - 99   1998.2

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:KINOKUNIYA CO LTD  

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  • On Roberts' counterexample to the fourteenth problem of Hilbert Reviewed

    H Kojima, M Miyanishi

    JOURNAL OF PURE AND APPLIED ALGEBRA   122 ( 3 )   277 - 292   1997.11

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    In [4], Roberts constructed a counterexample to the fourteenth problem of Hilbert as the invariant subring of the additive group scheme G(a) acting on a polynomial ring of dimension 7. We replace his combinatoric construction of the invariant elements by more straightforward construction using the invariant rational elements. (C) 1997 Elsevier Science B.V.

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Books

  • Algebraic varieties and automorphism groups

    増田 佳代, 岸本 崇, 小島 秀雄, 宮西 正宜, Zaidenberg Mikhail

    Mathematical Society of Japan  2017  ( ISBN:9784864970488

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  • 要点明解線形数学

    印南 信宏, 田中 環, 小島 秀雄, 星 明考

    培風館  2016  ( ISBN:9784563012007

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    Language:Japanese

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  • Affine algebraic geometry : proceedings of the conference, Osaka, Japan, 3-6 March 2011

    増田 佳代, 小島 秀雄, 岸本 崇, Conference on Affine Algebraic Geometry

    World Scientific  2013  ( ISBN:9789814436694

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  • 要点明解線形数学

    吉原 久夫, 印南 信宏, 田中 環, 小島 秀雄

    培風館  2006  ( ISBN:4563003611

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MISC

  • Smooth factorial affine surfaces of logarithmic Kodaira dimension zero with trivial units

    Gene Freudenburg, Hideo Kojima, Takanori Nagamine

    2019.10

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    Publishing type:Internal/External technical report, pre-print, etc.  

    This paper considers the family $\mathscr{S}_0$ of smooth affine factorial<br />
    surfaces of logarithmic Kodaira dimension 0 with trivial units over an<br />
    algebraically closed field $k$. Our main result (Theorem 4.1) is that the<br />
    number of isomorphism classes represented in $\mathscr{S}_0$ is at least<br />
    countably infinite. This contradicts the earlier classification of Gurjar and<br />
    Miyanishi [5] which asserted that $\mathscr{S}_0$ has at most two elements up<br />
    to isomorphism when $k=\mathbb{C}$. Thus, the classification of surfaces in<br />
    $\mathscr{S}_0$ for the field $\mathbb{C}$, long thought to have been settled,<br />
    is an open problem.

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  • Closed polynomials and their applications for computations of kernels of monomial derivations

    Chiaki Kitazawa, Hideo Kojima, Takanrori Nagamine

    2018.7

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    Publishing type:Internal/External technical report, pre-print, etc.  

    In this paper, we give some results on closed polynomials and factorially<br />
    closed polynomial in $n$ variables. In particular, we give a characterization<br />
    of factorially closed polynomials in $n$ variables over an algebraically closed<br />
    field for any characteristic. Furthermore, as an application of results on<br />
    closed polynomials, we determine kernels of non-zero monomial derivations on<br />
    the polynomial ring in two variables over a UFD. Finally, by using this result,<br />
    for a field $k$, we determine the non-zero monomial derivations $D$ on $k[x,y]$<br />
    such that the quotient field of the kernel of $D$ is not equal to the kernel of<br />
    $D$ in $k(x,y)$.

    arXiv

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Presentations

  • Some results on open algebraic surfaces of logarithmic Kodaira dimension zero Invited

    Hideo Kojima

    Kinosaki Algebraic Geometry Symposium 2019  2109.10 

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    Event date: 2019.10

    Language:English   Presentation type:Oral presentation (invited, special)  

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  • Rational open surfaces of log Kodaira dimension ≤ 1 Invited

    Hideo Kojima

    RIMS Symposia: Rational points on higher dimensional varieties  2019.12 

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    Language:English   Presentation type:Oral presentation (invited, special)  

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  • Closed polynomials over integral domains

    Hideo Kojima

    The 1st Asian International Conference in Science (UTAR, NU, and CYCU)  2019.11 

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    Language:English   Presentation type:Oral presentation (general)  

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  • Logarithmic plurigenera of smooth affine surfaces Invited International conference

    Hideo Kojima

    Algebraic surfaces and related topics  2019.8 

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    Language:English   Presentation type:Oral presentation (invited, special)  

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  • Normal log canonical del Pezzo surfaces of rank one

    Hideo Kojima

    2018.9 

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    Language:Japanese   Presentation type:Oral presentation (general)  

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  • Normal log canonical del Pezzo surfaces of rank one Invited International conference

    Hideo Kojima

    Algebraic Geometry – Mariusz Koras in memoriam  2018.5 

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  • Complements of plane curves with logarithmic Kodaira dimension zero Invited International conference

    Hideo Kojima

    Polynomial Rings and Affine Algebraic Geometry  2018.2 

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  • Qホモロジー射影平面上の単尖点有理曲線について

    小島秀雄

    代数学ミニシンポジウム2017  2017.9 

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    Language:Japanese   Presentation type:Oral presentation (general)  

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  • 対数的小平次元がゼロとなる開代数曲面について Invited

    小島秀雄

    第62回代数学シンポジウム  2017.9 

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  • Normal del Pezzo surfaces of rank one with log canonical singular points Invited International conference

    Hideo Kojima

    The 15th Affine Algebraic Geometry Meeting  2017.3 

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  • Some results on open algebraic surfaces of log Kodaira dimension zero Invited

    Hideo Kojima

    2017.1 

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    Language:Japanese   Presentation type:Oral presentation (invited, special)  

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  • Some results on open algebraic surfaces of log Kodaira dimension zero Invited

    Hideo Kojima

    Workshop on Galois point and related topics  2016.6 

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    Language:Japanese   Presentation type:Oral presentation (invited, special)  

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  • Some results on open algebraic surfaces of non-negative logarithmic Kodaira dimension Invited International conference

    Hideo Kojima

    KIAS-TIFR-ICTS Joint Advanced School of Algebraic Surfaces and Related Topics  2015.11 

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Research Projects

  • Structure and logarithmic plurigenera of normal affine surfaces

    Grant number:21K03200

    2021.4 - 2024.3

    System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

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    Grant amount:\4160000 ( Direct Cost: \3200000 、 Indirect Cost:\960000 )

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  • 開代数曲面と正規代数曲面の研究

    2017.4 - 2020.3

    System name:科学研究費 基盤研究(C)

    Awarding organization:日本学術振興会

    小島秀雄

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    Authorship:Principal investigator  Grant type:Competitive

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  • Structural analysis of the automorphism group of a polynomial ring and its application

    Grant number:15K04826

    2015.4 - 2019.3

    System name:Grants-in-Aid for Scientific Research

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    Kuroda Shigeru, Kojima Hideo, Tanimoto Ryuji

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    Grant amount:\4810000 ( Direct Cost: \3700000 、 Indirect Cost:\1110000 )

    A polynomial is an indispensable concept in mathematics, and the ring formed by them is a basic object in modern algebra. However, there remain various difficult open problems concerning polynomial rings, which have been studied worldwide. In the study of such problems, automorphisms of a polynomial ring and the ring formed by them play important roles. In this research, we investigated subgroups of the automorphism group of a polynomial ring and related objects, and obtained various new information about them. We also succeeded in constructing a new counterexample to Hilbert's fourteenth problem by using the knowledge of polynomial automorphisms.

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  • 対数的小平次元が1以下となる開代数曲面と正規代数曲面の構造解明

    2014.4 - 2017.3

    System name:科学研究費 基盤研究(C)

    Awarding organization:日本学術振興会

    小島秀雄

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  • 高次元アフィン代数多様体の構造とユニポテント幾何

    2012.4 - 2017.3

    System name:科学研究費 基盤研究 (B)

    Awarding organization:日本学術振興会

    宮西正宜

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    Grant type:Competitive

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  • Study on Glois embedding of surface of non-general type

    Grant number:24540036

    2012.4 - 2016.3

    System name:Grants-in-Aid for Scientific Research

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    Yoshihara Hisao, TOKUNAGA Hiroo, KONDO Shigeyuki, KONNO Kazuhiro, KOJIMA Hideo

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    Grant amount:\5070000 ( Direct Cost: \3900000 、 Indirect Cost:\1170000 )

    We have studied Galois points for plane curves and some hypersurfaces, after that we have generalized the concept of it and defined Galois embedding of algebraic varieties. Here we study on the Galois embeddings of conclete algebraic varieties. For elliptic curve we embedd it by complete linear system and study the arrangement of Galois lines. For algebraic surface of non-general type we consider if there exists the Galois embedding, in paticular bi-elliptic surface has no Galois embedding. In case some algebraic variety has no Galois embedding, we consider the Galois closure variety, especially we take such variety as smooth cubic.

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  • アフィン代数多様体の構造解明とその応用

    2011.4 - 2014.3

    System name:科学研究費 若手研究(B)

    Awarding organization:日本学術振興会

    小島秀雄

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  • Study on the various structures of algebraic surfaces by Galois embeddings

    Grant number:21540033

    2009 - 2011

    System name:Grants-in-Aid for Scientific Research

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    YOSHIHARA Hisao, TOKUNAGA Hiroo, KONDO Shigeyuki, KONNO Kazuhiro, KOJIMA Hideo

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    Grant amount:\4420000 ( Direct Cost: \3400000 、 Indirect Cost:\1020000 )

    Suppose an abelian surface A has a Galois embedding. Then, what is the least number n such that A is embedded into the projective n-space? The answer is 7 and moreover such an abelian surface is isomorphic to E×E, where E is an elliptic curve. We considered also the questions for curves. For the plane curve with genus 1 we found the Galois group when it has a Galois point, for the space elliptic curve we found it has always Galois lines.

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  • 開代数曲面の分類とその応用

    2008.4 - 2011.3

    System name:科研費 若手研究(B)

    Awarding organization:日本学術振興会

    小島秀雄

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  • Study on the Galois embeddings of K3 surfaces

    Grant number:19540016

    2007 - 2008

    System name:Grants-in-Aid for Scientific Research

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    YOSHIHARA Hisao, KONDO Shigeyuki, KONNO Kazuhiro, TOKUNAGA Hiroo, SEKIGAWA Kouei, TAKATA Toshie, KOJIMA Hideo

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    Grant amount:\4420000 ( Direct Cost: \3400000 、 Indirect Cost:\1020000 )

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  • 対数的小平次元が非負となる開代数曲面に関する研究

    2005.4 - 2008.3

    System name:科研費 若手研究(B)

    Awarding organization:日本学術振興会

    小島秀雄

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    Authorship:Principal investigator  Grant type:Competitive

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  • Complex analysis of residues currents and computational algebraic analysis

    Grant number:17540150

    2005 - 2007

    System name:Grants-in-Aid for Scientific Research

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    TAJIMA Shinichi, YOSHIHARA Hisao, KOJIMA Hideo, TAKEUCHI Kiyoshi, NAKAMURA Yayoi

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    Grant amount:\3630000 ( Direct Cost: \3300000 、 Indirect Cost:\330000 )

    Hypersurface isolated singularities and associated residues currents are considered in the context of algebraic analysis.
    ・An efficient algorithm that computes bases of a dual vector space of a Milnor algebra associated to a singular point has been constructed.
    ・A new method for computing standard bases of a zero-dimensional ideal in a power series ring has been proposed. The key ingredient in this approach is the concept of algebraic local cohomology and the Grothendieck local duality.
    ・An algorithm for construction holonomic D-modules attached to hypersurface isolated singularities has been derived and the structure of these holonomic D-modules have been investigated.
    ・An algorithmic method for computing homological indices of holomorphic vector fields has been proposed.

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  • Study on Galois embeddings of algebraic surfaces

    Grant number:17540018

    2005 - 2006

    System name:Grants-in-Aid for Scientific Research

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    YOSHIHARA Hisao, OHBUCHI Akira, KONNO Kazuhiro, TOKUNAGA Hiro-o, TAKATA Toshie, KOJIMA Hideo

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    Grant amount:\3100000 ( Direct Cost: \3100000 )

    We have studied the Galois embedding of algebraic curves and surfaces, especially rational curves and abelian surfaces.
    In the case of abelian surfaces we have obtained all the possible types of the Galois groups which can appear as the covering transformation groups. Moreove we listed a lot of examples of abelian surfaces with given Galois groups of embeddings. In particular we have shown that such abelian surfaces are isogenous to the products of two elliptic curves. On the other hand, we have found the least number N such that abelinan surfaces have the embeddings into PAN. Concernig this study we have studied for singular plane rational curves. We determined all possible type of Galois group, i.e., they are cyclic, dihedral, A_4, S_4 and S_4 and have shown the examples with such Galois groups. Connecting with this research, we have studied if the Galois automorphism can be extended to a birational transformation or not. As a result we have obtained that there are a lot of rational curves such that the autopmorphism cannot be extended to birational transformation, for example we found rational curve with only nodes as singularities and the degree is bigger than 7 with outer Galois point.

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  • Research on space curve and its Galois line

    Grant number:15540016

    2003 - 2004

    System name:Grants-in-Aid for Scientific Research

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    YOSHIHARA Hisao, HOMMA Masaaki, OHBUCHI Akira, AKIYAMA Shigeki, TOKUNAGA Hiro-o, KOJIMA Hideo

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    Grant amount:\3400000 ( Direct Cost: \3400000 )

    Let C, L and L_0 be a curve and lines in the projective three space P^3 respectively. Consider a projection p_L:P^3--→L_0 with center L, where L and L_0 have no intersection. Restricting p_L to C, we get a morphism p_L|C:C--→L_0 and an extension of fields:k(C)/k(L_0). We have studied the algebraic structure of the extension and the geometric one of C. If this extension is Galois, then we call L a Galois line. In particular we have studied the structure of the Galois group and the number of Galois lines for some special cases, for example, we obtained that the number is at most one if the degree of C is a prime number. After completed the first aims, we started to study the following research : Let V be a smooth projective variety and D be a very ample divisor. Let f:V--→ P^N be the projective embedding associated with |D|. Consider a projection p with a center W such that dim W=N-n-1 and f(V) does not meet W. Ifp f:V--→ P^n induces a Galois extension of function fields, then (V,D) is said to define a Galois embedding. Under this condition we have shown several properties of the Galois group of the covering. After general discussions we study the subject for abelian surfaces in detail.

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  • Algebraic Analysis of residue currents and an algorithm for computing Noether operators

    Grant number:15540159

    2003 - 2004

    System name:Grants-in-Aid for Scientific Research

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    TAJIMA Shinichi, OAKU Toshinori, KOJIMA Hidoe

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    Grant amount:\2400000 ( Direct Cost: \2400000 )

    We have investigated Noether operators attached to a zero-dimensional primary ideal, the associated algebraic local cohomology and Grothendieck duality in the context of algebraic analysis. We have studies the structure of holonomic D-modules attached to a quasi-Homogeneous isolated singularity.
    1.A concept of Noether operators attaced to a zero-dimensional primary ideal is introduced. Their fundamental properties are clarified. An algorithm that compute Noether operator basis. are derived.
    2.An algorithm for computing holonomic D-module that leads zero-dimensional algebraic local cohomology class is constructed.
    3.Hermite-Jacobi reproducing kernel is investigated. A method for computing dual basis w.r.t. Grothendieck duality is constructed.
    4.A new method that compute Grothendieck local residue is derived.
    5.Semi quasi-homogeneous isolated singularities with inner modarity (at most) four are considered. Holonomic D-modules attached to these singularities are investigated. The factthat he multiplicity of such holonomic system is equal to the difference of Milnor number and Tjurina namber has proved by case by case computation.
    Besides, we have investigated Noether operator attaced to higher dimensional primary ideal and residue currents.

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  • 正規アフィン代数曲面の構造に関する研究

    2002.4 - 2005.3

    System name:科研費 若手研究(B)

    Awarding organization:日本学術振興会

    小島秀雄

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    Authorship:Principal investigator  Grant type:Competitive

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  • 商特異点を持つ代数曲面と多項式環の不変部分環について

    Grant number:97J05048

    1998 - 1999

    System name:科学研究費助成事業

    Research category:特別研究員奨励費

    Awarding organization:日本学術振興会

    小島 秀雄

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    Grant amount:\1800000 ( Direct Cost: \1800000 )

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Teaching Experience

  • 数学の世界

    2022
    Institution name:新潟大学

  • 地域創生科学演習

    2022
    Institution name:新潟大学

  • 先端科学技術総論

    2022
    Institution name:新潟大学

  • 理学スタディ・スキルズ

    2021
    -
    2022
    Institution name:新潟大学

  • 専門力アクティブ・ラーニング

    2021
    Institution name:新潟大学

  • 先端科学技術総論

    2020
    -
    2022
    Institution name:新潟大学

  • 代数系IA

    2017
    Institution name:新潟大学

  • 数学基礎B2

    2017
    Institution name:新潟大学

  • 代数入門B

    2017
    Institution name:新潟大学

  • 代数系IB

    2017
    Institution name:新潟大学

  • 数学基礎B1

    2017
    Institution name:新潟大学

  • 代数入門A

    2017
    Institution name:新潟大学

  • 集合と写像

    2017
    -
    2018
    Institution name:新潟大学

  • 自然科学総論Ⅰ

    2017
    Institution name:新潟大学

  • 数理科学研究発表〔外部発表〕(数学)

    2015
    Institution name:新潟大学

  • くらしと数理

    2014
    -
    2019
    Institution name:新潟大学

  • 数学基礎B

    2014
    -
    2016
    Institution name:新潟大学

  • 数理科学セミナーⅠ(数学)

    2014
    Institution name:新潟大学

  • 数理科学研究発表演習〔中間発表〕(数学)

    2014
    Institution name:新潟大学

  • 数理科学文献詳読Ⅰ(数学)

    2014
    Institution name:新潟大学

  • 数理物質科学特定研究Ⅰ(数学)

    2014
    Institution name:新潟大学

  • 代数幾何学

    2013
    Institution name:新潟大学

  • 数学講究

    2013
    Institution name:新潟大学

  • 代数構造特論

    2013
    Institution name:新潟大学

  • 情報基礎数学I

    2013
    -
    2018
    Institution name:新潟大学

  • 代数系I

    2013
    -
    2016
    Institution name:新潟大学

  • 代数入門

    2013
    -
    2016
    Institution name:新潟大学

  • 代数系II

    2013
    Institution name:新潟大学

  • 数理科学文献詳読Ⅱ(数学)

    2012
    -
    2015
    Institution name:新潟大学

  • 数理科学セミナーⅡ(数学)

    2012
    -
    2015
    Institution name:新潟大学

  • 数理物質科学特定研究Ⅱ(数学)

    2012
    -
    2015
    Institution name:新潟大学

  • 情報工学特定研究Ⅱ

    2012
    Institution name:新潟大学

  • 応用数理C

    2012
    Institution name:新潟大学

  • 自然科学総論Ⅲ

    2011
    Institution name:新潟大学

  • 応用数理B

    2010
    -
    2011
    Institution name:新潟大学

  • 工学リテラシー入門(情報工学科)

    2009
    -
    2013
    Institution name:新潟大学

  • 情報工学演習

    2009
    Institution name:新潟大学

  • アドバンススキルズ

    2008
    -
    2013
    Institution name:新潟大学

  • ベーシックスキルズ

    2008
    Institution name:新潟大学

  • 構造数理

    2007
    -
    2014
    Institution name:新潟大学

  • 基礎数理A II

    2007
    -
    2012
    Institution name:新潟大学

  • 応用代数学特論

    2007
    -
    2012
    Institution name:新潟大学

  • アフィン代数幾何学

    2007
    -
    2012
    Institution name:新潟大学

  • 基礎数理A I

    2007
    -
    2012
    Institution name:新潟大学

  • 基礎数理BII

    2007
    -
    2009
    Institution name:新潟大学

  • 基礎数理BI

    2007
    -
    2008
    Institution name:新潟大学

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