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K3 surfaces and related algebraic varieties

Research Project

Project/Area Number 20340002
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionHiroshima University

Principal Investigator

SHIMADA Ichiro  広島大学, 大学院・理学研究科, 教授 (10235616)

Co-Investigator(Kenkyū-buntansha) KIMURA Shun-ichi  広島大学, 大学院・理学研究科, 教授 (10284150)
ISHII Akira  広島大学, 大学院・理学研究科, 准教授 (10252420)
TAKAHASHI Nobuyoshi  広島大学, 大学院・理学研究科, 准教授 (60301298)
TAKAHASHI Hiroki  広島大学, 大学院・理学研究科, 准教授 (90291476)
SUMIHIRO Hideyasu  広島大学, 大学院・理学研究科, 名誉教授 (60068129)
HIRANOUCHI Toshiro  広島大学, 大学院・理学研究科, 助教 (30532551)
伊藤 浩行  広島大学, 大学院・工学研究院, 准教授 (60232469)
松本 眞  広島大学, 大学院・理学研究科, 教授 (70231602)
Co-Investigator(Renkei-kenkyūsha) MATSUMOTO Makoto  東京大学, 大学院・数理科学研究科, 教授 (70231602)
ITO Hiroyuki  東京理科大学, 理工学部 (60232469)
MUTSUMI Saito  北海道大学, 大学院・理学研究科, 教授 (70215565)
OKA Mutsuo  東京理科大学, 理学部 (40011697)
KONDO Shigeyuki  名古屋大学, 大学院・多元数理科学研究科 (50186847)
MATSUMOTO Keiji  北海道大学, 大学院・理学研究科, 教授 (30229546)
TERAO Hiroaki  北海道大学, 大学院・理学研究科, 教授 (90119058)
ISHIKAWA Goo  北海道大学, 大学院・理学研究科, 教授 (50176161)
Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥15,860,000 (Direct Cost: ¥12,200,000、Indirect Cost: ¥3,660,000)
Fiscal Year 2011: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2010: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2009: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2008: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
KeywordsK3曲面 / ネロン・セヴェリ格子 / 超越格子 / 6次曲線 / 超特異K3曲面 / 射影モデル / 平面6次曲線 / 基本群 / 格子理論 / 超特異性 / フロベニウス固有値 / 単有理性 / 2次剰余符号 / 分岐被覆 / ザリスキ・ファンカンペン / 単純K3特異点 / 有理2重点 / ザリスキペア / ザリスキ・ファンカンペンの定理
Research Abstract

By writing various computer programs for the computational research of lattices and applying them to lattices of algebraic cycles on K3 surfaces(or related algebraic varieties), we obtained many geometric consequences. In particular, we classified the Zariski pairs of simple plane curves of degree 6 by introducing a notion of Z-splitting curves, and described their adjacency relations. We also presented an algorithm to determine the primitivity of a lattice of algebraic curves in the lattice of topological cycles for a given complex algebraic surface.

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (121 results)

All 2012 2011 2010 2009 2008 Other

All Journal Article (56 results) (of which Peer Reviewed: 56 results) Presentation (63 results) Remarks (2 results)

  • [Journal Article] A note on rational normal curves totally tangent to aHermitian variety2012

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Designs, Codes and Cryptography

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Frobenius in cidence varieties of linear subspaces over finitefields2012

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Finite Fields and Their Applications

      Volume: 18 Pages: 337-361

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A note onderived categories of Fermat varieties, Proceedings of the conference2012

    • Author(s)
      Akira Ishii and Kazushi Ueda
    • Journal Title

      "DereivedCategories Tokyo 2011", EMS series of Congress Reprots

      Volume: 掲載決定

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Nonstandard point counting for algebraic varieties2012

    • Author(s)
      Nobuyoshi Takahashi
    • Journal Title

      Communications in Algebra

      Volume: 掲載決定

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Motivic zeta functions in additive monoidal categories2012

    • Author(s)
      Ken-taro Kimura, Shun-ichi Kumura, and Nobuyoshi Takahashi
    • Journal Title

      Journal of K-Theory

      Volume: 掲載決定

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Milnor K-groups modulo p^n of a complete discrete valuationfield2012

    • Author(s)
      Toshiro Hiranouchi
    • Journal Title

      Proc. Japan Acad., Ser. A

      Volume: 掲載決定

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Rationality of Motivic Chow series modulo A^1-homotopy2012

    • Author(s)
      E. Javier Elizondo and Shun-ichi Kimura
    • Journal Title

      Advances in Mathematics

      Volume: 掲載決定

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Frobenius incidence varieties of linear subspaces over finite fields2012

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Finite Fields and Their Applications

      Volume: 18 Issue: 2 Pages: 337-361

    • DOI

      10.1016/j.ffa.2011.09.004

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on rational normal curves totally tangent to a Hermitian variety2012

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Designs, Codes and Cryptography

      Volume: (掲載決定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Finite dimensional morphisms in atensor category2011

    • Author(s)
      Pedro Luis del Angel and Shun-ichi Kimura
    • Journal Title

      J. Reine Angew. Math

      Volume: 656 Pages: 213-222

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A noteon consistency conditions on dimer models2011

    • Author(s)
      Akira Ishii and Kazushi Ueda
    • Journal Title

      Higher dimensional algebraic geometry, 143. 164, RIMS Kokyuroku Bessatsu

      Volume: B24

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Descending chain condition for stringy invariants. Higher dimensional algebraic geometry2011

    • Author(s)
      Nobuyoshi Takahashi
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B24 Pages: 165-178

    • NAID

      110008429992

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability conditions on An-singularities2010

    • Author(s)
      Akira Ishii, Kazushi Ueda and Hokuto Uehara
    • Journal Title

      J. Differential Geom

      Volume: 84no.1 Pages: 87-126

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Ramification of truncated discrete valuation rings : a survey2010

    • Author(s)
      Toshiro Hiranouchi
    • Journal Title

      Algebraic number theory and related topics 2008, RIMS Kokyuroku Bessatsu, B19, Res. Inst. Math. Sci.(RIMS), Kyoto

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Class field theory for open curves over p-adic fields2010

    • Author(s)
      Toshiro Hiranouchi
    • Journal Title

      Math. Z

      Volume: 226no.1 Pages: 107-113

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Pure weight perfect modules on divisorial schemes2010

    • Author(s)
      Toshiro Hiranouchi and Satoshi Mochizuki
    • Journal Title

      Deformation spaces, Aspects Math., Vieweg+ Teubner, Wiesbaden

      Volume: E40

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Flat modules and Grobner basesover truncated discrete valuation rings2010

    • Author(s)
      Toshiro Hiranouchi and YuichiroTaguchi
    • Journal Title

      Interdiscip. Inform. Sci

      Volume: 16no.1 Pages: 33-37

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Primitivity of sublattices generated by classes of curves on an algebraic surface2010

    • Author(s)
      Ichiro Shimada and Nobuyoshi Takahashi
    • Journal Title

      Comment. Math. Univ. St. Pauli

      Volume: 59no.2 Pages: 77-95

    • NAID

      110007887251

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lattice Zariski k-ples of plane sextic curves and Z-splitting curves for double plane sextics2010

    • Author(s)
      Ichiro Shimada
    • Journal Title

      MichiganMath. J

      Volume: 59-no.3 Pages: 621-665

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Topology of curves ona surface and lattice-theoretic invariantsof coverings of the surface2010

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Algebraic geometry in East Asia. Seoul 2008

      Volume: 60 Pages: 361-382

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Generalized Zariski-van Kampen theorem and its application to Grassmannian dual varieties2010

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Internat. J. Math

      Volume: 21no.5 Pages: 591-637

    • NAID

      120002598782

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Primitivity of sublattices generated by classes of curves on an algebraic surface.2010

    • Author(s)
      I. Shimada, N. Takahashi
    • Journal Title

      Comment.Math.Univ.St.Pauli 59

      Pages: 77-95

    • NAID

      110007887251

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Lattice Zariski k-pies of plane sextic curves and Z-splitting curves for double plane sextics.2010

    • Author(s)
      I. Shimada
    • Journal Title

      Michigan Math.J. 59, no.3

      Pages: 621-665

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Topology of curves on a surface and lattice-theoretic invariants of coverings of the surface.2010

    • Author(s)
      I. Shimada
    • Journal Title

      Algebraic geometry in East Asia-Seoul 2008, Adv.Stud.Pure Math., Math.Soc.Japan 60

      Pages: 361-382

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Generalized Zariski-van Kampen theorem and its application to Grassmannian dual varieties.2010

    • Author(s)
      I. Shimada
    • Journal Title

      Internat.J.Math. 21, no.5

      Pages: 591-637

    • NAID

      120002598782

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Primitivity of sublattices generated by classes of curves on an algebraic surface.2010

    • Author(s)
      Ichiro Shimada, Nobuyoshi Takahashi
    • Journal Title

      Comment.Math.Univ.St.Pauli

      Volume: 59 Pages: 77-95

    • NAID

      110007887251

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Topology of curves on a surface and lattice-theoretic invariants of coverings of the surface2010

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Adv.Stud.Pure Math.

      Volume: 60 Pages: 361-382

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lattice Zariski k-ples of plane sextic curves and Z-splitting curves for double plane sextics2010

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Michigan Math.J.

      Volume: 59 Pages: 621-665

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized Zariski-van Kampen theorem and its application to Grassmannian dual varieties2010

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Internat.J.Math.

      Volume: 21 Pages: 591-637

    • NAID

      120002598782

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Topology of curves on a surface and lattice-theoretic invariants of coverings of the surface2010

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Adv.Stud.Pure Math. (掲載決定, 印刷中)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lattice Zariski k-pies of plane sextic curves and Z-splitting curves for double plane sextics2010

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Michigan Math.J. (掲載決定, 印刷中)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized Zariski-van Kampen theorem and its application to Grassmannian dual varieties2010

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Internat.J.Math. (掲載決定, 印刷中)

    • NAID

      120002598782

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Surjectivity of thecycle map for Chow motives. Motives and algebraic cycles2009

    • Author(s)
      Shun-ichi Kimura
    • Journal Title

      Fields Inst. Commun

      Volume: 50 Pages: 157-165

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Smallness of fundamental groups for arithmetic schemes2009

    • Author(s)
      Shinya Harada and Toshiro Hiranouchi
    • Journal Title

      J. Number Theory

      Volume: 129no.1 Pages: 27-32

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Irrationality of motivic series of Chow varieties2009

    • Author(s)
      E. Javier Elizondo and Shun-Ichi Kimura
    • Journal Title

      Math. Z

      Volume: 263no.1 Pages: 27-32

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Zariski-van Kampen method and transcendental lattices of certain singular K3 surfaces2009

    • Author(s)
      Ken-ichiro Arima and Ichiro Shimada
    • Journal Title

      Tokyo J. Math

      Volume: 32no.1 Pages: 201-227

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Transcendental lattices and supersingular reduction lattices of a singular K3 surface2009

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Trans. Amer. Math. Soc

      Volume: 361no.2 Pages: 909-949

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Hilbert-Speisertype imaginary quadratic fields2009

    • Author(s)
      Humio Ichimura and Hiroki Sumida-Takahashi
    • Journal Title

      Acta Arith

      Volume: 136no.4 Pages: 385-389

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Non-homeomorphic conjugate complex varieties.2009

    • Author(s)
      I. Shimada
    • Journal Title

      Singularities Niigata-Toyama 2007, Adv.Stud.Pure Math., Math.Soc.Japan 56

      Pages: 285-301

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Non-homeomorphic conjugate complex varieties2009

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Adv.Stud.Pure Math. 56

      Pages: 285-301

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Zariski-van Kampen method and transcendental lattices of certain singular K3 surfaces2009

    • Author(s)
      Ken-ichiro Arima
    • Journal Title

      Tokyo J.Math. 32

      Pages: 201-227

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Transcendental lattices and supersingular reduction lattices of a singular K3 surface.2009

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Trans. Amer. Math. Soc. 361

      Pages: 909-949

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Relative Pro -l Completions of Mapping Class Groups2009

    • Author(s)
      Richard Hain
    • Journal Title

      Journal of Algebra (受理済み)

      Pages: 36-36

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Totally free arrangements of hyperplanes2009

    • Author(s)
      Takuro Abe
    • Journal Title

      Proc. Amer. Math. Soc. 131

      Pages: 1405-1410

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On moduli spaces of quiver representations associated with dimer models2008

    • Author(s)
      Akira Ishii and Kazushi Ueda
    • Journal Title

      Higherdimensional algebraic varieties and vector bundles, 127. 141, RIMS Kokyuroku Bessatsu

      Volume: B9

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Singularities of dual varieties in characteristic 2.2008

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Adv. Stud. Pure Math. 50

      Pages: 299-331

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On arithmetic Zariski pairs in degree 62008

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Adv. Geom. 8

      Pages: 205-225

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Topology of polar weighted homogeneous hypersurfaces2008

    • Author(s)
      Mutsuo Oka
    • Journal Title

      Kodai Math. J. 31

      Pages: 163-182

    • NAID

      130004687885

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Efficient jump ahead for F2-linear random number generators2008

    • Author(s)
      Hiroshi Haramoto
    • Journal Title

      INFORMS J. Comput. 20

      Pages: 385-390

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Error correcting sequence and projective de Bruijn graph2008

    • Author(s)
      Mariko Hagita
    • Journal Title

      Graphs Combin. 24

      Pages: 185-194

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Periodicity of hyperplane arrangements with integral coefficients modulo positive integers2008

    • Author(s)
      Hidehiko Kamiya
    • Journal Title

      J. Algebraic Combin. 27

      Pages: 317-330

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Euler multiplicity and addition-deletion theorems for multi-arrangements2008

    • Author(s)
      Takuro Abe
    • Journal Title

      J. Lond. Math. Soc. 77

      Pages: 335-348

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global classification of curves on the symplectic plane2008

    • Author(s)
      Goo Ishikawa
    • Journal Title

      Contemp. Math. 459

      Pages: 51-72

    • NAID

      120006459528

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generic singularities of implicit systems of first order differential equations on the plane2008

    • Author(s)
      A. A. Davydov
    • Journal Title

      Jpn. J. Math. 3

      Pages: 93-119

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-homeomorphic conjugate complex varieties

    • Author(s)
      Ichiro Shimada
    • Journal Title

      Adv. Stud. Pure Math. (受理済み)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Zariski-van Kampen method and transcendental lattices of certain singular K3 surfaces

    • Author(s)
      Ken-ichiro Arima
    • Journal Title

      Tokyo J. Math. (受理済み)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] On iterated G-Hilbert schemes2012

    • Author(s)
      石井亮
    • Organizer
      高次元代数多様体とベクトル束の代数幾何学
    • Place of Presentation
      九州大学数理学研究院
    • Year and Date
      2012-03-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Rationality and irrationality of motivic series2012

    • Author(s)
      木村俊一
    • Organizer
      Workshop on p. Adic arithmetic geometry and, motives, 23January
    • Place of Presentation
      東北大学
    • Year and Date
      2012-01-23
    • Related Report
      2011 Final Research Report
  • [Presentation] McKay correspondence and dimer models2012

    • Author(s)
      石井亮
    • Organizer
      Mini-workshop of Algebra
    • Place of Presentation
      国立台湾大学,台湾
    • Related Report
      2011 Final Research Report
  • [Presentation] Dimer models and crepant resolutions2011

    • Author(s)
      石井亮
    • Organizer
      Noncommutative Algebraic Geometry and D-branes
    • Place of Presentation
      Simons Center for Geometry and Physics, Stony Brook University, USA
    • Year and Date
      2011-12-13
    • Related Report
      2011 Final Research Report
  • [Presentation] 超特異K3曲面の次数2の射影モデルについて2011

    • Author(s)
      島田伊知朗
    • Organizer
      代数幾何ワークショップ
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2011-12-08
    • Related Report
      2011 Final Research Report
  • [Presentation] 超特異K3曲面の次数2の射影モデルについて2011

    • Author(s)
      島田伊知朗
    • Organizer
      代数幾何ワークショップ
    • Place of Presentation
      東京大学大学院数理科学研究科(招待講演)
    • Year and Date
      2011-12-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] Special McKay correspondence and exceptional collections2011

    • Author(s)
      石井亮
    • Organizer
      Complex Algebraic Geometry
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach, Germany
    • Year and Date
      2011-09-26
    • Related Report
      2011 Final Research Report
  • [Presentation] Rationality and irrationality of motivic Chow series2011

    • Author(s)
      木村俊一
    • Organizer
      O' Sullivan Conference, 2 September
    • Place of Presentation
      オーストラリア国立大学,オーストラリア
    • Year and Date
      2011-09-02
    • Related Report
      2011 Final Research Report
  • [Presentation] A remark on invertible polynomials and exceptional collections2011

    • Author(s)
      石井亮
    • Organizer
      WORKSHOP ON NON-COMMUTATIVE GEOMETRY AND THE McKAY CORRESPONDENCE
    • Place of Presentation
      名古屋大学多元数理科学研究科
    • Year and Date
      2011-03-14
    • Related Report
      2011 Final Research Report
  • [Presentation] Supersingular K3 surfaces in characteristic 52011

    • Author(s)
      島田伊知朗
    • Organizer
      代数幾何学研究集会-ファノ多様体と正標数上の話題を中心として-, 21 February
    • Place of Presentation
      九州大学伊都キャンパス数理学研究教育棟
    • Year and Date
      2011-02-21
    • Related Report
      2011 Final Research Report
  • [Presentation] Supersingular K3 surfaces in characteristic 52011

    • Author(s)
      島田伊知朗
    • Organizer
      代数幾何学研究集会-ファノ多様体と正標数上の話題を中心として-
    • Place of Presentation
      九州大学(招待講演)
    • Year and Date
      2011-02-21
    • Related Report
      2010 Annual Research Report
  • [Presentation] 標数5における超特異K3曲面2011

    • Author(s)
      島田伊知朗
    • Organizer
      日本数学会中四国支部, 29 January
    • Place of Presentation
      鳴門地場産業振興センター
    • Year and Date
      2011-01-29
    • Related Report
      2011 Final Research Report
  • [Presentation] 標数5における超特異K3曲面2011

    • Author(s)
      島田伊知朗
    • Organizer
      日本数学会中四国支部会
    • Place of Presentation
      鳴門地場産業振興センター
    • Year and Date
      2011-01-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] Supersingular K3 surfaces and lattice theory2011

    • Author(s)
      島田伊知朗
    • Organizer
      Arithmetic and Algebraic Geometry 2011, 21 January
    • Place of Presentation
      University of Tokyo
    • Year and Date
      2011-01-21
    • Related Report
      2011 Final Research Report
  • [Presentation] Supersingular K3 surfaces and lattice theory2011

    • Author(s)
      Ichiro Shimada
    • Organizer
      Arithmetic and Algebraic Geometry 2011
    • Place of Presentation
      東京大学(招待講演)
    • Year and Date
      2011-01-21
    • Related Report
      2010 Annual Research Report
  • [Presentation] On the image of the cyclemap for the product of elliptic curves over ap-adic feld2010

    • Author(s)
      平之内俊郎
    • Organizer
      Industrious number theory 3, Korea Institute for Advanced Study
    • Place of Presentation
      Seoul(Korea)
    • Year and Date
      2010-11-12
    • Related Report
      2011 Final Research Report
  • [Presentation] 超特異代数多様体について2010

    • Author(s)
      島田伊知朗
    • Organizer
      日本数学会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-24
    • Related Report
      2011 Final Research Report
  • [Presentation] 超特異代数多様体について2010

    • Author(s)
      島田伊知朗
    • Organizer
      日本数学会
    • Place of Presentation
      名古屋大学(招待講演)
    • Year and Date
      2010-09-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] 小さい標数における超特異K3曲面の構成2010

    • Author(s)
      島田伊知朗
    • Organizer
      玉原特殊多様体研究集会
    • Place of Presentation
      玉原国際セミナーハウス
    • Year and Date
      2010-09-08
    • Related Report
      2011 Final Research Report
  • [Presentation] 小さい標数における超特異K3曲面の構成2010

    • Author(s)
      島田伊知朗
    • Organizer
      玉原特殊多様体研究集会
    • Place of Presentation
      玉原国際セミナーハウス(招待講演)
    • Year and Date
      2010-09-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] Special McKay correspondence and universal localisation2010

    • Author(s)
      石井亮
    • Organizer
      Geometry and algebra of orbifolds and the McKay correspondence
    • Place of Presentation
      Warwick Univ., U. K.
    • Year and Date
      2010-08-12
    • Related Report
      2011 Final Research Report
  • [Presentation] 小さい標数における超特異K3曲面について2010

    • Author(s)
      島田伊知朗
    • Organizer
      代数幾何研究集会2010
    • Place of Presentation
      法政大学小金井キャンパス
    • Year and Date
      2010-07-17
    • Related Report
      2011 Final Research Report
  • [Presentation] 小さい標数における超特異K3曲面の構成2010

    • Author(s)
      島田伊知朗
    • Organizer
      代数幾何研究集会2010
    • Place of Presentation
      法政大学(招待講演)
    • Year and Date
      2010-07-17
    • Related Report
      2010 Annual Research Report
  • [Presentation] Lattices of algebraic cycles in positive characteristics2010

    • Author(s)
      島田伊知朗
    • Organizer
      5th Pacific Rim Conference on Mathematics
    • Place of Presentation
      Stanford University, USA
    • Year and Date
      2010-07-02
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Lattices of algebraic cycles in positive characteristics2010

    • Author(s)
      Ichiro Shimada
    • Organizer
      5th Pacific Rim Conference on Mathematics
    • Place of Presentation
      Stanford University, アメリカ(招待講演)
    • Year and Date
      2010-07-02
    • Related Report
      2010 Annual Research Report
  • [Presentation] Dimer models and exceptionalcollections2010

    • Author(s)
      石井亮
    • Organizer
      DMM seminar
    • Place of Presentation
      東京大学IPMU
    • Year and Date
      2010-04-26
    • Related Report
      2011 Final Research Report
  • [Presentation] Lattices of algebraic cycleson varieties of Fermat type(joint workwith Nobuyoshi Takahashi)2010

    • Author(s)
      島田伊知朗
    • Organizer
      Algebraic Geometry in Characteristic p and Related Topics
    • Place of Presentation
      University of Tokyo
    • Year and Date
      2010-02-19
    • Related Report
      2011 Final Research Report
  • [Presentation] Lattices of algebraic cycles on varieties of Fermat type2010

    • Author(s)
      島田伊知朗
    • Organizer
      Algebraic Geometry in Positive Characteristic and Related Topics
    • Place of Presentation
      東京大学数理科学研究所
    • Year and Date
      2010-02-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] Supersingular K3 surfaces and lattice theory2010

    • Author(s)
      I. Shimada
    • Organizer
      Arithmetic and Algebraic Geometry 2011
    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2010-01-21
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On lattice-invariants of complex algebraic surfaces and theirb applications slides2009

    • Author(s)
      島田伊知朗
    • Organizer
      Symposium in algebraic geometry
    • Place of Presentation
      Busan, Korea
    • Year and Date
      2009-12-28
    • Related Report
      2011 Final Research Report
  • [Presentation] On lattice-invariants of complex algebraic surfaces and their applications2009

    • Author(s)
      I. Shimada
    • Organizer
      Symposium in algebraic geometry
    • Place of Presentation
      Busan, Korea
    • Year and Date
      2009-12-28
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On lattice-invariants of complex algebraic surfaces and their applications2009

    • Author(s)
      島田伊知朗
    • Organizer
      Symposium in algebraic geometry
    • Place of Presentation
      Busan, 韓国
    • Year and Date
      2009-12-28
    • Related Report
      2009 Annual Research Report
  • [Presentation] Descending chain condition for stringy invariants2009

    • Author(s)
      高橋宣能
    • Organizer
      高次元代数幾何の周辺
    • Place of Presentation
      京都大学理学部
    • Year and Date
      2009-12-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Dimer models and exceptional collections2009

    • Author(s)
      石井亮
    • Organizer
      Mirror Symmetry and Gromov-Witten Invariants
    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2009-12-07
    • Related Report
      2011 Final Research Report
  • [Presentation] 超特異K3曲面と格子理論2009

    • Author(s)
      島田伊知朗
    • Organizer
      代数学と計算
    • Place of Presentation
      首都大学東京
    • Year and Date
      2009-12-04
    • Related Report
      2011 Final Research Report 2009 Annual Research Report
  • [Presentation] Transcendental lattices of complex algebraic surfaces2009

    • Author(s)
      島田伊知朗
    • Organizer
      Tohoku-Fudan joint symposium on algebraic geometry
    • Place of Presentation
      Tohoku University
    • Year and Date
      2009-11-25
    • Related Report
      2011 Final Research Report
  • [Presentation] Transcendental lattices of complex algebraic surfaces2009

    • Author(s)
      島田伊知朗
    • Organizer
      Tohoku-Fudan joint symposium on algebraic geometry
    • Place of Presentation
      東北大学(宮城県)
    • Year and Date
      2009-11-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] Transcendenlatl lattices of surfaces, Workshop2009

    • Author(s)
      島田伊知朗
    • Organizer
      Category Theory, Computer Science and Topology
    • Place of Presentation
      信州大学
    • Year and Date
      2009-10-18
    • Related Report
      2011 Final Research Report
  • [Presentation] Transcendenlatl lattices of surfaces2009

    • Author(s)
      島田伊知朗
    • Organizer
      Workshop "Category Theory, Computer Science and Topology"
    • Place of Presentation
      信州大学(長野県)
    • Year and Date
      2009-10-18
    • Related Report
      2009 Annual Research Report
  • [Presentation] Dimer models and tilting bundles2009

    • Author(s)
      石井亮
    • Organizer
      Complex Algebraic Geometry
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach, Germany
    • Year and Date
      2009-10-01
    • Related Report
      2011 Final Research Report
  • [Presentation] Remarks on Zariski pairsof surfaces in the projective space2009

    • Author(s)
      島田伊知朗
    • Organizer
      Seminar Talk
    • Place of Presentation
      Fudan University, ShangHai, China
    • Year and Date
      2009-09-24
    • Related Report
      2011 Final Research Report
  • [Presentation] Zariski pairs of normal surfaces in P^32009

    • Author(s)
      島田伊知朗
    • Organizer
      The 5th Franco-Japanese Symposium on Singularities
    • Place of Presentation
      IRMA, Strasbourg, France
    • Year and Date
      2009-08-27
    • Related Report
      2011 Final Research Report
  • [Presentation] Zariski pairs of normal surfaces in P32009

    • Author(s)
      島田伊知朗
    • Organizer
      The 5th Franco-Japanese Symposium on Singularities
    • Place of Presentation
      IRMA, Strasbourg, フランス
    • Year and Date
      2009-08-27
    • Related Report
      2009 Annual Research Report
  • [Presentation] On lattice-theoretic invariants of curves on a surface2009

    • Author(s)
      島田伊知朗
    • Organizer
      The 2ndMSJ-SI Arrangements of Hyperplanes
    • Place of Presentation
      Hokkaido University, Sapporo
    • Year and Date
      2009-08-12
    • Related Report
      2011 Final Research Report
  • [Presentation] On lattice-theoretic invariants of curves on a surface2009

    • Author(s)
      I. Shimada
    • Organizer
      The 2nd MSJ-ST ArranaPments of Hypernlanes
    • Place of Presentation
      北海道大学
    • Year and Date
      2009-08-12
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On lattice-theoretic invariants of curves on a surface2009

    • Author(s)
      島田伊知朗
    • Organizer
      The 2nd MSJ-SI Arrangements of Hyperplanes
    • Place of Presentation
      北海道大学
    • Year and Date
      2009-08-12
    • Related Report
      2009 Annual Research Report
  • [Presentation] 相対Gromov-Witten不変量2009

    • Author(s)
      高橋宣能
    • Organizer
      代数幾何学サマースクール2009
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2009-07-28
    • Related Report
      2011 Final Research Report
  • [Presentation] Dimer models and the special McKay correspondence2009

    • Author(s)
      石井亮
    • Organizer
      Algebraic Triangulated Categories and Related Topics
    • Place of Presentation
      RIMS(京都大学)
    • Year and Date
      2009-07-24
    • Related Report
      2011 Final Research Report
  • [Presentation] Links of hypersurface simple K3 singularities (joint work with A. Katanaga)2009

    • Author(s)
      島田伊知朗
    • Organizer
      Hodge theory and algebraic geometry
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-07-03
    • Related Report
      2009 Annual Research Report
  • [Presentation] Zariski pairs and lattice theory2009

    • Author(s)
      島田伊知朗
    • Organizer
      Antalya Algebra Days XI
    • Place of Presentation
      Antalya, トルコ
    • Year and Date
      2009-05-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] Zariski pairs and lattice theory2009

    • Author(s)
      島田伊知朗
    • Organizer
      Antalya Algebra Days XI
    • Place of Presentation
      Antalya, Turk
    • Year and Date
      2009-03-24
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Zariski pairs and lattice theory2009

    • Author(s)
      島田伊知朗
    • Organizer
      General Seminar
    • Place of Presentation
      Bilkent University, Ankara, Turk
    • Year and Date
      2009-03-18
    • Related Report
      2011 Final Research Report
  • [Presentation] Splitting curves for thedouble covering branching along a planecurve of degree 62009

    • Author(s)
      島田伊知朗
    • Organizer
      第4回代数・解析・幾何学セミナー
    • Place of Presentation
      鹿児島大学
    • Year and Date
      2009-02-18
    • Related Report
      2011 Final Research Report
  • [Presentation] Splitting curves for the double covering branching along a plane curve of degree 62009

    • Author(s)
      Ichiro Shimada
    • Organizer
      第4回代数・解析・幾何学セミナー
    • Place of Presentation
      鹿児島大学理学部
    • Year and Date
      2009-02-18
    • Related Report
      2008 Annual Research Report
  • [Presentation] Splitting curves for thedouble covering branching along a planecurve of degree 62009

    • Author(s)
      島田伊知朗
    • Organizer
      IIandIII,特異点セミナー
    • Place of Presentation
      東京理科大学
    • Year and Date
      2009-01-23
    • Related Report
      2011 Final Research Report
  • [Presentation] On equisingular families of plane curves of degree 62009

    • Author(s)
      島田伊知朗
    • Organizer
      Arithmetic and Algebraic Geometry Related to Moduli Spaces
    • Place of Presentation
      University of Tokyo
    • Year and Date
      2009-01-19
    • Related Report
      2011 Final Research Report
  • [Presentation] On equisingular families of plane curves of degree 62009

    • Author(s)
      Ichiro Shimada
    • Organizer
      Arithmetic and Algebraic Geometry Related to Moduli Spaces
    • Place of Presentation
      東京大学数理科学研究所
    • Year and Date
      2009-01-19
    • Related Report
      2008 Annual Research Report
  • [Presentation] Generalized Zariski-van Kampen theorem and its application to Grassmannian dual varieties2008

    • Author(s)
      Ichiro Shimada
    • Organizer
      Conference on Topology-Geometry-Algebra-Arithmetic
    • Place of Presentation
      Dalat University, Vietnam
    • Year and Date
      2008-12-22
    • Related Report
      2008 Annual Research Report
  • [Presentation] 擬似乱数検定における、サンプルサイズ調整の自動2008

    • Author(s)
      松本 眞
    • Organizer
      平成20年度統計数理研究所 乱数重点型共同研究第2回研究会
    • Place of Presentation
      統計数理研究所
    • Year and Date
      2008-12-13
    • Related Report
      2008 Annual Research Report
  • [Presentation] FINITE DIMENSIONALITY OF THE MOTIVES AND RATIONALITY OF THE MOTIVIC ZETA2008

    • Author(s)
      木村俊一
    • Organizer
      International Symposium on Automorphic Forms, L -Functions and Shimura Varieties
    • Place of Presentation
      Inha University, korea
    • Year and Date
      2008-11-25
    • Related Report
      2008 Annual Research Report
  • [Presentation] Generalized Zariski-van Kampen theorem2008

    • Author(s)
      Ichiro Shimada
    • Organizer
      Algebraic Geometry in East Asia
    • Place of Presentation
      Korean Inst, Adv. Studies, korea
    • Year and Date
      2008-11-13
    • Related Report
      2008 Annual Research Report
  • [Presentation] Splitting curves for double sextic planes2008

    • Author(s)
      Ichiro Shimada
    • Organizer
      Algebraic Geometry in Positive Characteristics and Related Topics
    • Place of Presentation
      名古屋大学多元数理科学研究所
    • Year and Date
      2008-11-07
    • Related Report
      2008 Annual Research Report
  • [Presentation] Generating uniform real random numbers in IEEE 754 specification via affine transition2008

    • Author(s)
      松本 眞
    • Organizer
      Monte Carlo and Quasi Monte Carlo 2008
    • Place of Presentation
      モントリオール大学(カナダ)
    • Year and Date
      2008-07-09
    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.sci.hiroshima-u.ac.jp/~shimada/K3.html

    • Related Report
      2011 Final Research Report
  • [Remarks] ホームページ

    • URL

      http://www.math.sci.hiroshima-u.ac.jp/~shimada/index.html

    • Related Report
      2010 Self-evaluation Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

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