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The moduli space of cubic surfaces via Hessian K3 surfaces

Research Project

Project/Area Number 22740007
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionUniversity of Yamanashi

Principal Investigator

KOIKE Kenji  山梨大学, 教育人間科学部, 准教授 (20362056)

Project Period (FY) 2010 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2010: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Keywords3次曲面 / K3曲面 / テータ関数 / 塩田-猪瀬構造 / Kummer曲面 / 楕円曲面 / HessianK3曲面
Research Abstract

We studied Hessian K3 surfaces of cubic surfaces of non-Sylvester types. They are obtained also as toric hypersurfaces, and considered as a mirror family of(2, 2, 2)-hypersurfaces of(P^1)^3. Their period integrals satisfy the Lauricella's hypergeometeric differential equations F_C, and the period domain is the Siegel upper half space of degree two.

Report

(3 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • Research Products

    (4 results)

All 2011 Other

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

  • [Journal Article] Hessian K3 surfaces of non-Sylvester type2011

    • Author(s)
      Kenji Koike
    • Journal Title

      Journal of Algebra

      Volume: vol.330 Pages: 388-403

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Elliptic K3 surfaces admitting a Shioda-Inose structure

    • Author(s)
      Kenji Koike
    • Journal Title

      Commentarii Mathematici Universitatis Sancti Pauli

      Volume: (掲載予定)

    • NAID

      110009595203

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Presentation] 楕円的K3曲面と塩田-猪瀬構造2011

    • Author(s)
      小池健二
    • Organizer
      第5回玉原特殊多様体研究集会
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2011-09-06
    • Related Report
      2011 Final Research Report
  • [Presentation] 楕円的K3曲面と塩田-猪瀬構造2011

    • Author(s)
      小池健二
    • Organizer
      第5回玉原特殊多様体研究集会
    • Place of Presentation
      東京大学玉原国際セミナーハウス(群馬県沼田市)
    • Year and Date
      2011-09-06
    • Related Report
      2011 Annual Research Report

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Published: 2010-08-23   Modified: 2016-04-21  

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