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Study of Kahler Ricci flows

Research Project

Project/Area Number 24540092
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionSophia University

Principal Investigator

TSUJI Hajime  上智大学, 理工学部, 教授 (30172000)

Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywordsケーラー・リッチ流 / ベルグマン核 / 随伴直線束 / 多重劣調和関数 / ケーラー多様体 / 極小モデル / フランス / パリ / 極値的体積形式 / 標準測度 / 半正値性 / 国際研究交流 / ケーラー・アインシュタイン計量 / 複素多様体
Outline of Final Research Achievements

We study the family of fiberwise Kaehler-Ricci flows on a smooth projective family of projective varieties with pseudoeffective canonical classes. We have proven that if the initial form is a Kaehler form on the total space, the resulting family of Kahler-Ricci flows preserves the semipositivity. The method is the approximation of the Kaehler-Ricci flows in terms of the dynamical system of Bergman kernels and then apply the logarithmic plurisubharmonic variation properties of Bergman kernels due to B. Berndtsson. This resul can be viewed as a refinement of the semiposity of the direct image of pluri adjoint line bundles.

This reserch is a joint project with S. Boucksom in Ecole Polytechnic in Paris.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (13 results)

All 2015 2014 2013 2012 Other

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (9 results) (of which Invited: 7 results) Book (2 results)

  • [Journal Article] On the extremal measure on a complex manifold2015

    • Author(s)
      H. Tsuji
    • Journal Title

      Progress in Mathematics

      Volume: 308 Pages: 159-175

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some dynamical systems of extremal measures2015

    • Author(s)
      H.Tsuji
    • Journal Title

      Proc. of KSCV 10

      Volume: 未定

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Presentation] Invariance of plurigenera in K\"ahler case2015

    • Author(s)
      H. Tsuji
    • Organizer
      Colloquium talk
    • Place of Presentation
      Ecole polytechnique (Paris)
    • Year and Date
      2015-03-12
    • Related Report
      2014 Annual Research Report
  • [Presentation] Stablity of pluricanonical systems of K\"ahler fibrations2014

    • Author(s)
      H. Tsuji
    • Organizer
      複素幾何学菅平シンポジウム
    • Place of Presentation
      菅平高原 プチホテルゾンタック
    • Year and Date
      2014-11-07
    • Related Report
      2014 Annual Research Report
  • [Presentation] Some dynamical systems of extremal measures2014

    • Author(s)
      H. Tsuji
    • Organizer
      KCSV 10
    • Place of Presentation
      慶州 コロンホテル
    • Year and Date
      2014-08-10
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] A new invaraiant measure in complex geometry2014

    • Author(s)
      Hajime Tsuji
    • Organizer
      The Shoshichi .Kobayashi Memorial Symposium
    • Place of Presentation
      東京大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Dynamical systems of extremal measures2013

    • Author(s)
      Hajime Tsuji
    • Organizer
      Extremal Kaeher metrics
    • Place of Presentation
      CRM (Montreal, Canada)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Semipositivity of invariant measures2013

    • Author(s)
      Hajime Tsuji
    • Organizer
      Rational Points, Rational Curves and Entire Holomorphic Curves on Algebraic Varieties
    • Place of Presentation
      CRM (Motreal Canada)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Constructions of canonical singular hermitian metrics on relative adjoint bundles2013

    • Author(s)
      Hajime Tsuji
    • Organizer
      KIAS Complex Geometry Symposium
    • Place of Presentation
      KIAS Seoul
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] A Schwarz type lemma for canonical measure on a family of projective manifolds with nonnegative Kodaira dimension2013

    • Author(s)
      Hajime TSUJI
    • Organizer
      CRM workshop Extremal Kaehler Metrics
    • Place of Presentation
      CRM Motreal Canada
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Schawarz type lemma for canonical measures

    • Author(s)
      辻 元
    • Organizer
      複素幾何菅平シンポジウム
    • Place of Presentation
      長野県菅平高原
    • Related Report
      2012 Research-status Report
    • Invited
  • [Book] 複素多様体論講義2013

    • Author(s)
      辻 元
    • Total Pages
      230
    • Publisher
      サイエンス社
    • Related Report
      2013 Research-status Report
  • [Book] 複素多様体論講義2012

    • Author(s)
      辻 元
    • Total Pages
      207
    • Publisher
      サイエンス社
    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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