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Study of vector bundles on algebraic varieties

Research Project

Project/Area Number 19540034
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

SUMIHIRO Hideyasu  Hiroshima University, 大学院・理学研究科, 名誉教授 (60068129)

Co-Investigator(Kenkyū-buntansha) ISHII Akira  広島大学, 大学院・理学研究科, 准教授 (10252420)
KIMURA Shunichi  広島大学, 大学院・理学研究科, 准教授 (10284150)
KITADAI Yukinori  広島大学, 大学院・工学研究科, 特任助教 (30511563)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords代数幾何学 / 代数学 / ベクトル束 / Frobenius写像 / ベクトル束の分解問題 / Hartshorne予想 / 小平消滅定理 / ペクトル束
Research Abstract

Lange-Pauly proved that the direct images of line bundles on non-singular projective curve with genus greater than or equal 2 are semi-stable. We extended this result to semi-stable vector bundles on non-singular curves and non-singular projective surfaces. As a corollary, we get a new result on geography of non-singular minimal surfaces of general type in positive characteristics. Further, We obtained a new theorem for rank two vector bundles on 4-dimensional projective space to split into line bundles.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (23 results)

All 2010 2009 2008 2007 Other

All Journal Article (9 results) (of which Peer Reviewed: 9 results) Presentation (14 results)

  • [Journal Article] Stability conditions on An singularities2010

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

      J. Differential Geometry Vol.84

      Pages: 87-126

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On moduli spaces of quiver representations associated with dimmer modules2008

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

      RIMS Kokyuroku Bessatsu Vol.9

      Pages: 127-141

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Canonical filtrations and stability of direct images by Frobenius morphisms2008

    • Author(s)
      Yukinori Kitadai, Hideyasu Sumihiro
    • Journal Title

      Tohoku Math. J. Vol.60

      Pages: 287-301

    • NAID

      110006691412

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Canonical filtrations and stability of direct images by Frobenius morphisms II2008

    • Author(s)
      Yukinori Kitadai, Hideyasu Sumihiro
    • Journal Title

      Hiroshima Math. J. Vol.38

      Pages: 241-261

    • NAID

      110006794235

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Canonical filtrations and stability of direct images by Frobenius morphisms2008

    • Author(s)
      Yukinori Kitadai, Hid eyasu Sumihiro
    • Journal Title

      Tohoku Mathematical Journal 60

      Pages: 287-301

    • NAID

      110006691412

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Canonical filtrations and stability of direct images by Frobenius morphisms II2008

    • Author(s)
      Yukinori Kitadai, Hid eyasu Sumihiro
    • Journal Title

      Hiroshima Mathematical Journal 38

      Pages: 243-261

    • NAID

      110006794235

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Canonical filtrations and stability of direct images by Frobenius morphisms2008

    • Author(s)
      Yukinori Kitadai and Hideyasu Sumihiro
    • Journal Title

      Tohoku Mathematical Joumal 60(掲載決定)

    • NAID

      110006691412

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Canonical filtrations and stability of direct images by Frobenius morphims. II2008

    • Author(s)
      Yukinori Kitadai and Hideyasu Sumihiro
    • Journal Title

      Hiroshima Mathematical Journal 38(掲載決定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stability conditions on An-singurarities

    • Author(s)
      Akira Ishii, K. Ueda, H. Uehara
    • Journal Title

      J.Differential Geometry (掲載決定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] Dimer models and tiling bundles2009

    • Author(s)
      Akira Ishii
    • Organizer
      Complex Algebraic Geometry
    • Place of Presentation
      Mathematishes Forshungsitut Oberwolfach, Germany
    • Year and Date
      2009-10-01
    • Related Report
      2009 Final Research Report
  • [Presentation] Dimer models and tilting bundles2009

    • Author(s)
      Akira Ishii
    • Organizer
      mathematishes Forschungsinstitut Oberwolfach
    • Place of Presentation
      Oberwolfach Germany
    • Year and Date
      2009-10-01
    • Related Report
      2009 Annual Research Report
  • [Presentation] Dimer models and special McKay correspondence2009

    • Author(s)
      Akira Ishii
    • Organizer
      Algebraic Triangulated Categories and Related Topics
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-07-24
    • Related Report
      2009 Final Research Report
  • [Presentation] Dimer model and the special correspondence2008

    • Author(s)
      Akira Ishii
    • Organizer
      An International Conference in Algebraic Geometry
    • Place of Presentation
      東京大学
    • Year and Date
      2008-12-19
    • Related Report
      2009 Final Research Report
  • [Presentation] 余接束のフロベニウス写像による直像の安定性2008

    • Author(s)
      北臺如法, 隅広秀康
    • Organizer
      日本数学会年会
    • Place of Presentation
      近畿大学理工学部
    • Year and Date
      2008-03-26
    • Related Report
      2007 Annual Research Report
  • [Presentation] Stability condtitions on An singularities2008

    • Author(s)
      Akira Ishii
    • Organizer
      ICTS Conference on Vector Bundles, TIFR.
    • Place of Presentation
      Mumbai India
    • Year and Date
      2008-03-07
    • Related Report
      2009 Final Research Report
  • [Presentation] Stability conditions on A_n singularities2008

    • Author(s)
      Akira Ishii
    • Organizer
      ICTS Conference on Vector Bundles
    • Place of Presentation
      TIFR, Mumbai
    • Year and Date
      2008-03-07
    • Related Report
      2007 Annual Research Report
  • [Presentation] Bipartite graphs on tori and crepant resolutions2008

    • Author(s)
      石井 亮
    • Organizer
      第3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
      2008-02-19
    • Related Report
      2007 Annual Research Report
  • [Presentation] On brane tilings and crepant resolutions2008

    • Author(s)
      石井 亮
    • Organizer
      トーリック多様体の理論の展開と応用
    • Place of Presentation
      東北大学大学院理学研究科
    • Year and Date
      2008-01-12
    • Related Report
      2007 Annual Research Report
  • [Presentation] Brane tilings and crepant resolutioins of some three-dimensional toric singularities2007

    • Author(s)
      Akira Ishii
    • Organizer
      Categorical Aspects of Algebric Geometry in Mirror Symmtry
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-12-07
    • Related Report
      2009 Final Research Report
  • [Presentation] Brane tilings and crepant resolutions of some three-dimensional toric singularities2007

    • Author(s)
      Akira Ishii
    • Organizer
      Categorical Aspects of Algebraic Geometry in Mirror Symmetry
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-12-07
    • Related Report
      2007 Annual Research Report
  • [Presentation] Stability of direct images of cotangent bundles by Frobenius morphisms2007

    • Author(s)
      北臺如法
    • Organizer
      代数幾何学城崎シンポジウム, ポスターセッション
    • Place of Presentation
      城崎大会議館
    • Year and Date
      2007-10-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] Brane tilings and moduli of quiver representations (with K. Ueda)2007

    • 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科
    • Year and Date
      2007-09-12
    • Related Report
      2007 Annual Research Report
  • [Presentation] On the moduli of quiver representations associated with brane tilings2007

    • Author(s)
      石井 亮
    • Organizer
      高次元代数多様体とベクトル束
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-07-03
    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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