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Explicit constructions of several algebraic varieties

Research Project

Project/Area Number 20540042
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

NAKAYAMA Noboru  京都大学, 数理解析研究, 准教授 (10189079)

Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords代数幾何 / 代数学 / 代数幾何学 / 代数多様体 / 自己正則写像
Research Abstract

Two results are obtained by applying explicit constructions to the classification problem of surfaces which admit non-isomorphic surjective endomorphisms. One is the case of normal projective complex surfaces, and the classification has been completed except for the case of some special rational surfaces. The other is the case of non-singular projective surfaces in positive characteristic, and we have also certain classification results assuming that the endomorphisms are separable.

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

    (17 results)

All 2010 2009 2008

All Journal Article (14 results) (of which Peer Reviewed: 14 results) Presentation (3 results)

  • [Journal Article] Separable endomorphisms of surfaces in positive characteristic2010

    • Author(s)
      Noboru Nakayama
    • Journal Title

      Adv. Stud. Pure Math

      Volume: vol.60 Pages: 301-330

    • URL

      http://mathsoc.jp/publication/ASPM/contents/CFM60.pdf

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Intersection sheaves over normal schemes2010

    • Author(s)
      Noboru Nakayama
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 62 Issue: 2 Pages: 487-595

    • DOI

      10.2969/jmsj/06220487

    • NAID

      10026999128

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Polarized endomorphisms of complex normal varieties2010

    • Author(s)
      Noboru Nakayama
    • Journal Title

      Math. Ann

      Volume: 346 Issue: 4 Pages: 991-1018

    • DOI

      10.1007/s00208-009-0420-y

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Polarized endomorphisms of complex normal varietie2010

    • Author(s)
      Noboru Nakayama, De-Qi Zhang
    • Journal Title

      Math.Ann. 346

      Pages: 991-1018

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Intersection sheaves over normal schemes2010

    • Author(s)
      Noboru Nakayama
    • Journal Title

      J.Math.Soc.Japan 62

      Pages: 487-595

    • NAID

      10026999128

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Separable endomorphisms of surfaces in positive characteristic2010

    • Author(s)
      Noboru Nakayama
    • Journal Title

      Adv.Stud.Pure Math. 60

      Pages: 301-330

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Polarized endomorphisms of complex normal varieties2010

    • Author(s)
      Noboru Nakayama
    • Journal Title

      Math.Ann.

      Volume: 346 Pages: 991-1018

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Intersection sheaves over normal schemes2010

    • Author(s)
      Noboru Nakayama
    • Journal Title

      J.Math.Soc.Japan

      Volume: 62 Pages: 487-595

    • NAID

      10026999128

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Separable endomorphisms of surfaces in positive characteristic2010

    • Author(s)
      Noboru Nakayama
    • Journal Title

      Adv.Stud.Pure Math., Math.Soc.Japan

      Volume: 60 Pages: 301-330

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Building blocks of etale endomorphisms of complex projective manifolds2009

    • Author(s)
      Noboru Nakayama, De-Qi Zhang
    • Journal Title

      Proc. London Math. Soc.

      Volume: 99 Issue: 3 Pages: 725-756

    • DOI

      10.1112/plms/pdp015

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Building blocks of etale endomorphisms of complex projective manifolds2009

    • Author(s)
      Noboru Nakayama, De-Qi Zhang
    • Journal Title

      Proc.London Math.Soc. 99

      Pages: 725-756

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Building blocks of etale endomorphisms of complex projective manifolds2009

    • Author(s)
      Noboru Nakayama
    • Journal Title

      Proc.London Math.Soc. 99

      Pages: 725-756

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Complex projective manifolds which admit non-isomorphic surjective endomorphsms2008

    • Author(s)
      Yoshio Fujimoto, Noboru Nakayama
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B9 Pages: 51-79

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Complex projective manifolds which admit non-isomorphic surjective endomorphsms2008

    • Author(s)
      Yoshio Fujimoto
    • Journal Title

      RIMS Kokyuroku Bessatsu B9

      Pages: 51-79

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Normal projective surfaces admitting non-isomorphic surjective endomorphisms2008

    • Author(s)
      Noboru Nakayama
    • Organizer
      Normal projective surfaces admitting non-isomorphic surjective endomorphisms
    • Place of Presentation
      Korea
    • Year and Date
      2008-11-12
    • Related Report
      2011 Final Research Report
  • [Presentation] Normal projective surfaces admitting non-isomorphic surjective endo-morphisms2008

    • Author(s)
      Noboru Nakayama
    • Organizer
      Algebraic Geometry in East Asia
    • Place of Presentation
      Korea Institute for Advanced Study
    • Year and Date
      2008-11-12
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Normal projective surfaces admitting non-isomorphic surjective endomorphisms2008

    • Author(s)
      Noboru Nakayama
    • Organizer
      Algebraic Geometry in East Asia
    • Place of Presentation
      Korea Institute for Advanced Study
    • Year and Date
      2008-11-12
    • Related Report
      2008 Annual Research Report

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

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