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ルート系を実現する代数多様体―ワイル群が支配する双有理幾何を目指して―

Research Project

Project/Area Number 20654004
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionKyoto University

Principal Investigator

向井 茂  京都大学, 数理解析研究所, 教授 (80115641)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2010: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2009: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2008: ¥800,000 (Direct Cost: ¥800,000)
KeywordsEnriques曲面 / K3曲面 / Mathieu群 / Dynkin図式 / 随伴軌道 / 代数的ベクトル束 / ルート系 / モジュライ空間 / アーベル曲面 / 代数幾何学 / 高次元双有理幾何学 / Mordell-Weil格子
Research Abstract

K3曲面のsymplectic自己同型のなす有限群とMathieu群M24には面白い関係がある。前者はM24の中に軌道が5個以上になるように埋め込める(Mukai,1988年)。これのEnriques類似を永く探して来たが、6次交代群の作用するEnriques曲面の格子論的構成を契機として、研究を進展することができた。大橋久範君と共同で、Enriques曲面のMathieu型のsemi-symplectic作用を定義した。そして、Mathieu型semi-symplectic作用をもつ有限群はいつも6次対称群に埋め込めるだろうかという問題を考察した。9月のOberwolfachでの研究集会で中間発表をした。
Lie環の極小随伴軌道として現れる代数多様体の表示とそれを用いた単純Lie環の分類の可能性について、2月の表現論研究集会で発表した。

Report

(3 results)
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (18 results)

All 2011 2010 2009 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (13 results)

  • [Journal Article] Curves and symmetric spaces II2010

    • Author(s)
      Shigeru Mukai
    • Journal Title

      Ann.of Math.

      Volume: 172 Pages: 1539-1558

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerically trivial involutions of Kummer type of Enriques surfaces2010

    • Author(s)
      Shigeru Mukai
    • Journal Title

      Kyoto Math.J.

      Volume: 50 Pages: 889-902

    • NAID

      120005593653

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Curves and symmetric spaces, II2010

    • Author(s)
      Shigeru Mukai
    • Journal Title

      Ann.of Math. (掲載確定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Obstructions to deforming curves on a threefold, I : a generalization of Mumford's example and an application to Hom schemes2009

    • Author(s)
      Shigeru Mukai, Hirokazu Nasu
    • Journal Title

      J.Alg.Geom. 18

      Pages: 691-709

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Obstructions to deforming curves on a 3-fold, I-a generalization of Mumford's example and an application to Hom schemes-

    • Author(s)
      S. Mukai, H. Nasu
    • Journal Title

      J. Alg. Geom. (to appear掲載確定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Simple Lie algebras and Legendre varieties2011

    • Author(s)
      Shigeru Mukai
    • Organizer
      Nilpotent orbits and representation theory
    • Place of Presentation
      九州大学(招待講演)
    • Year and Date
      2011-02-20
    • Related Report
      2010 Annual Research Report
  • [Presentation] Enriques surfaces of type E72010

    • Author(s)
      Shigeru Mukai
    • Organizer
      Algebraic Geometry Symposium
    • Place of Presentation
      城崎(招待講演)
    • Year and Date
      2010-10-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] Enriques surfaces of type E72010

    • Author(s)
      Shigeru Mukai
    • Organizer
      Compact Moduli
    • Place of Presentation
      Georgia Univ., Athens(USA)(招待講演)
    • Year and Date
      2010-10-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] Enriques surfaces of type E72010

    • Author(s)
      Shigeru Mukai
    • Organizer
      Perspectives on Algebraic Varieties
    • Place of Presentation
      Trento (Italy)(招待講演)
    • Year and Date
      2010-09-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] Enriques surfaces with many semi-symplectic automorphisms2010

    • Author(s)
      Shigeru Mukai
    • Organizer
      Komplexe Analysis
    • Place of Presentation
      Oberwolfach(Germany)(招待講演)
    • Year and Date
      2010-09-05
    • Related Report
      2010 Annual Research Report
  • [Presentation] Enriques surfaces and root systems2010

    • Author(s)
      Shigeru Mukai
    • Organizer
      Fifth Pacific Rim Conference of Mathematics
    • Place of Presentation
      Stanford Univ., California (USA)(招待講演)
    • Year and Date
      2010-07-02
    • Related Report
      2010 Annual Research Report
  • [Presentation] Polarized K3 surfaces of genus 162010

    • Author(s)
      Shigeru Mukai
    • Organizer
      Moduli spaces in Algebraic Geometry
    • Place of Presentation
      Mathematishes Forschungsinstitut Oberwolfach, Germany
    • Year and Date
      2010-01-12
    • Related Report
      2009 Annual Research Report
  • [Presentation] K3 and Enriques surfaces (4 lectures)2010

    • Author(s)
      Shigeru Mukai
    • Organizer
      IMPNGA Summer School on Algebraic Geometry
    • Place of Presentation
      Bedlewo, (Poland)(招待講演)
    • Related Report
      2010 Annual Research Report
  • [Presentation] Enriques surfaces associated with Richelot isognies2009

    • Author(s)
      Shigeru Mukai
    • Organizer
      Invariants of Algebraic Varieties
    • Place of Presentation
      東京大学
    • Year and Date
      2009-11-23
    • Related Report
      2009 Annual Research Report
  • [Presentation] Numerically reflective involutions of Enriques surfaces2009

    • Author(s)
      Shigeru Mukai
    • Organizer
      Complex Algebraic Geometry
    • Place of Presentation
      Mathematishes Forschungsinstitut Oberwolfach, Germany
    • Year and Date
      2009-09-29
    • Related Report
      2009 Annual Research Report
  • [Presentation] Non-abelian Brill-Noether loci of curves and application to the unirationality of moduli of K3 surfaces2009

    • Author(s)
      Shigeru Mukai
    • Organizer
      Moduli
    • Place of Presentation
      Humboldt Univ., Berlin, Germany
    • Year and Date
      2009-08-28
    • Related Report
      2009 Annual Research Report
  • [Presentation] Unirationality of moduli spaces of polarized K3 surfaces2009

    • Author(s)
      Shigeru Mukai
    • Organizer
      Geometry of Algebraic Varieties
    • Place of Presentation
      Steklov Institute, Moscow, Russia
    • Year and Date
      2009-06-30
    • Related Report
      2009 Annual Research Report
  • [Presentation] Homologically trivial involutions and Shioda-Inose correspondences for U+U (2)2009

    • Author(s)
      Shigeru Mukai
    • Organizer
      Moduli and Discrete Groups
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-06-10
    • Related Report
      2009 Annual Research Report

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

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