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Geometry of Ricci-flat manifolds and moment maps

Research Project

Project/Area Number 19540067
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KONNO Hiroshi  The University of Tokyo, 大学院・数理科学研究科, 准教授 (20254138)

Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords微分幾何 / シンプレクティック幾何 / シンプレクティック多様体 / 幾何学的量子化 / ハイパーケーラー多様体 / モーメント写像 / ハイパーケーラー商 / 微分幾何学 / シンプレクティック幾何学
Research Abstract

We studied the topology of hyperkahler quotients by tori. We showed that we can take the norm square of the hyperkahler moment map as a Morse function under certain conditions. As a result we derived a formula for the Betti numbers and, under certain conditions, determined the cohomology ring. We also studied geometric quantization of flag manifolds. We constructed the one parameter family of Kahler polarization starting from the standard one and converging to the real polarization coming from the Gelfand-Cetlin integrable system at quantum level.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (22 results)

All 2010 2009 2008 2007 Other

All Journal Article (8 results) (of which Peer Reviewed: 4 results) Presentation (10 results) Remarks (4 results)

  • [Journal Article] The geometry of toric hyperkahler varieties2009

    • Author(s)
      Hiroshi Konno
    • Journal Title

      Contemporary Mathematics 460

      Pages: 241-260

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Morse theory fot toric hyperkahler orbifolds2009

    • Author(s)
      Hiroshi Konno
    • Journal Title

      Lecture Note Series in Math. (Department Math., Osaka Univ.) 9

      Pages: 217-226

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Morse theory for toric hyperkahler orbifolds, in Lecture Note Series in Mathematics2008

    • Author(s)
      H.Konno
    • Journal Title

      Osaka Univ 9

      Pages: 217-226

    • Related Report
      2010 Final Research Report
  • [Journal Article] Geometry of toric hyperkahler varieties2008

    • Author(s)
      H.Konno
    • Journal Title

      Contemporary Math. 480

      Pages: 241-260

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Morse theory for toric hyperkahler orbifolds, in Lecture Note Series in Mathematics2008

    • Author(s)
      H. Konno
    • Journal Title

      Osaka Univ. vol. 9

      Pages: 217-226

    • Related Report
      2009 Self-evaluation Report
  • [Journal Article] Geometry of toric hyperkahler varieties2008

    • Author(s)
      H. Konno
    • Journal Title

      Contemporary Math. vol. 480

      Pages: 241-260

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Geometry of toric hyperkahler varieties2008

    • Author(s)
      Hiroshi Konno
    • Journal Title

      Contemporary Mathematics 460(in press)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Morse theory for toric hyperkahler orbifolds2008

    • Author(s)
      Hiroshi Konno
    • Journal Title

      Proceedings of the workshop Complex Geometry in Osaka' to appear

    • Related Report
      2007 Annual Research Report
  • [Presentation] Convergence of Khler polarizations to real polarizations on flag varieties2010

    • Author(s)
      H.Konno
    • Organizer
      第16回複素幾何シンポジウム
    • Place of Presentation
      菅平
    • Year and Date
      2010-10-21
    • Related Report
      2010 Final Research Report
  • [Presentation] Convergence of Kahler polarizations to real polarizations on flagvarieties2010

    • Author(s)
      今野宏
    • Organizer
      第16回複素幾何シンポジウム
    • Place of Presentation
      菅平
    • Year and Date
      2010-10-21
    • Related Report
      2010 Annual Research Report
  • [Presentation] Morse theory for abelian hyperkahler quotients2009

    • Author(s)
      H.Konno
    • Organizer
      East Asian Symplectic Conference 2009
    • Place of Presentation
      Academia Sinica, Taiwan
    • Year and Date
      2009-05-09
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
  • [Presentation] Morse theory for abelian hyperkahler quotients2009

    • Author(s)
      今野宏
    • Organizer
      East Asia Symplectic Conference 2009
    • Place of Presentation
      Academia Sinica (台北, 台湾)
    • Year and Date
      2009-05-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] ハイパーケーラー商の幾何2009

    • Author(s)
      今野宏
    • Organizer
      研究集会 幾何構造の諸相
    • Place of Presentation
      名城大学
    • Year and Date
      2009-03-09
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
  • [Presentation] Morse theory for abelian hyperkahler quotients2008

    • Author(s)
      今野宏
    • Organizer
      第55回幾何学シンポジウム
    • Place of Presentation
      弘前大学
    • Year and Date
      2008-08-22
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
  • [Presentation] Morse theory for abelian hyperkahler quotients・ハイパーケーラー商の幾何2008

    • Author(s)
      今野宏
    • Organizer
      第55回幾何学シンポジウム・研究集会「幾何構造の諸相」
    • Place of Presentation
      弘前大学・名城大学
    • Related Report
      2008 Annual Research Report
  • [Presentation] Morse theory for abelian hyperkahler quotients2007

    • Author(s)
      H.Konno
    • Organizer
      Complex Geometry in Osaka
    • Place of Presentation
      大阪大学
    • Year and Date
      2007-11-04
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
  • [Presentation] Morse theory for abelian hyperkahler quotients2007

    • Author(s)
      Hiroshi Konno
    • Organizer
      国際研究集会'Complex Geometry in Osaka'
    • Place of Presentation
      大阪大学
    • Year and Date
      2007-11-04
    • Related Report
      2007 Annual Research Report
  • [Presentation] Geometry of toric hyperkahler varieties2007

    • Author(s)
      H.Konno
    • Organizer
      Symplectic Geometry
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-07-26
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
  • [Remarks] ホームページ等

    • URL

      http://www.ms.u-tokyo.ac.jp/teacher/konno.html

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

      http://www.ms.u-tokyo.ac.jp/teacher/konno.html

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.ms.u-tokyo.ac.jp/teacher/konno.html

    • Related Report
      2009 Self-evaluation Report
  • [Remarks]

    • URL

      http://www.ms.u-tokyo.ac.jp/teacher/konno.html

    • Related Report
      2009 Annual Research Report

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

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