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Group theoretic and arithmetic aspects on K3 surfaces

Research Project

Project/Area Number 16540010
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionThe University of Tokyo

Principal Investigator

OGUISO Keiji  The University of Tokyo, Math.Sci., Associate Professor, 大学院・数理科学研究科, 助教授 (40224133)

Co-Investigator(Kenkyū-buntansha) KAWAMATA Yujiro  The University of Tokyo, Math.Sci., Professor, 大学院・数理科学研究科, 教授 (90126037)
TERASAWA Tomohide  The University of Tokyo, Math.Sci., Associate Professor, 大学院・数理科学研究科, 助教授 (50192654)
HOSONO Shinobu  The University of Tokyo, Math.Sci., Associate Professor, 大学院・数理科学研究科, 助教授 (60212198)
MATSUO Atsushi  The University of Tokyo, Math.Sci., Associate Professor, 大学院・数理科学研究科, 助教授 (20238968)
Project Period (FY) 2004 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2005: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2004: ¥1,800,000 (Direct Cost: ¥1,800,000)
Keywordshyperkahler manifold / K3 surfaces / birational automorphism / Salem polynomial / Mordell-Weil group / entropy / tree group / almost abelian group / 双有理変換群 / 有限可解群 / 6次交代群 / リーチ格子 / 自己双有理型変換群 / サーレム数
Research Abstract

I have studied group theoretical aspects of the bimeromorphic (birational) automorphism group of a hyperkahler manifold with a help of arithmetical notion "Salem polynomial" and entropy. As a result, among other things, I have obtained the following results :
Theorem 1. Let M be a non-projective hyperkahler manifold.
Then, BicM is an almost abelian group of rank at most max(1,P(M)-1).
Theorem 2. Let M be a projective hyperkahler manifold and G be a subgroup of BicM.
Then, G satisfies either one of :
(i) G is an almost abelian group of rank at most max(1,P(M)-2) ;
(ii) G>Z*Z.

Report

(3 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • Research Products

    (21 results)

All 2006 2005 2004 Other

All Journal Article (21 results)

  • [Journal Article] Tits alternative in hyperkahler manifolds2006

    • Author(s)
      K.Oguiso
    • Journal Title

      Math. Research Letters 13

      Pages: 307-316

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Tits alternative in hypekahler manifolds2006

    • Author(s)
      K.Oguiso
    • Journal Title

      Math.Research Letters 13

      Pages: 307-316

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Tits alternatives in hyperkahler manifolds2006

    • Author(s)
      K.Oguiso
    • Journal Title

      Math.Res.Lett. 13

      Pages: 307-316

    • Related Report
      2005 Annual Research Report
  • [Journal Article] The alternating group of degree 6 in geometry of the leech lattice and K3 surfaces2005

    • Author(s)
      J.H.Keum, K.Oguiso, D.Q.Zhang
    • Journal Title

      Proc. London Math. Soc. 90

      Pages: 371-394

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The alternating group of degree 6 in geometry of the Leech lattice and K3 surfaces2005

    • Author(s)
      J.H.Keum, K.Oguiso, D.Q.Zhang
    • Journal Title

      Proc.London Math.Soc. 90

      Pages: 371-394

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The alternating group of degree 6 in geometry of the leech lattice and K3 surfaces2005

    • Author(s)
      J.H.Keum, K.Oguiso, D.Q.Zhang
    • Journal Title

      Proc.London Math.Soc. 90

      Pages: 371-394

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A characterization of the Fermat quartic K3 Surface by means of finite symmetries2005

    • Author(s)
      K.Oguiso
    • Journal Title

      Compositio Math. 141

      Pages: 404-424

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A characterization of the Fermat quartic K3 surface by means of finite symmetries2004

    • Author(s)
      K.Oguiso
    • Journal Title

      Compositio Math. 141

      Pages: 404-424

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The dual Kahlev cone of compact Kahler three folds2004

    • Author(s)
      T.Peternell, K.Oguiso
    • Journal Title

      Comm. Anal. Geom. 12

      Pages: 1131-1154

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Autoequiralences of derived categories of a K3 surface and monodromy transformations2004

    • Author(s)
      S.Hosono, B.Liau, K.Oguiso, S.T.Yau
    • Journal Title

      J. Algebraic Geom. 13

      Pages: 513-545

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Fourier-Mukai number of a K3 surface2004

    • Author(s)
      S.Hosono, B.Liau, K.Oguiso, S.T.Yau
    • Journal Title

      CRM Proc. Lecture Notes 38

      Pages: 177-192

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The dual Kahler cone of compact Kahler threefolds2004

    • Author(s)
      T.Peternell, K.Oguiso
    • Journal Title

      Comm.Anal.Geom. 12

      Pages: 1131-1154

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Autoequivalences of derived categories of a K3 surface and monodromy transformations2004

    • Author(s)
      S.Hosono, B.Lian, K.Oguiso, S.T.Yau
    • Journal Title

      J.Algebraic Geom. 13

      Pages: 513-545

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Fourier-Mukai number of a K3 surface2004

    • Author(s)
      S.Hosono, B.H.Lian, K.Oguiso, S.T.Yau
    • Journal Title

      CRM Proc.Lecture Notes 38

      Pages: 177-192

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The dual K*hler cone of compact K*hler threefold2004

    • Author(s)
      T.Peternell, K.Oguiso
    • Journal Title

      Comm.Anal.Geom. 12

      Pages: 1131-1154

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Auto equivalences of derived categories of a K3 surface and monodromy transformations2004

    • Author(s)
      S.Hosono, B.Lian, K.Oguiso, S.T.Yau
    • Journal Title

      J.Alg.Geom. 13

      Pages: 513-545

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Fourier-Mukai number of a K3 surface2004

    • Author(s)
      S.Hosono, B.Lian, K.Oguiso, S.T.Tau
    • Journal Title

      CRM Proceedings and Lecture Notes 38

      Pages: 177-192

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Groups of automorphisms of null-entropy of hyperkahler manifolds : In the proceedings of Dolgachev 60

    • Author(s)
      K.Oguiso
    • Journal Title

      Contemporary Math (アクセプト済)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Extensions of the alternating group of degree 6 in geometry of K3 surfaces

    • Author(s)
      J.H.Keum, K.Oguiso, D.Q.Zhang
    • Journal Title

      European J.Combinatrics (アクセプト済)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] The Alternating Group of degree 6 in Geometry of the Leech Lattice and K3 surfaces

    • Author(s)
      J.H.Keum, K.Oguiso, D.-θ.Zhang
    • Journal Title

      Proc.London Math.Soc. (to appear)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A characterization of the Fermat quartic K3 surface by means of finite symmetries

    • Author(s)
      K.Oguiso
    • Journal Title

      Compositio Math. (to appear)

    • Related Report
      2004 Annual Research Report

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Published: 2004-04-01   Modified: 2016-04-21  

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