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The study of ideal limits of sequences of test configurations

Research Project

Project/Area Number 25610012
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionOsaka University

Principal Investigator

MABUCHI TOSHIKI  大阪大学, その他部局等, 名誉教授 (80116102)

Co-Investigator(Kenkyū-buntansha) 二木 昭人  東京大学, 大学院数理科学研究科, 教授 (90143247)
Co-Investigator(Renkei-kenkyūsha) NAKAGAWA Yasuhiro  佐賀大学, 大学院工学研究科, 教授 (90250662)
NITTA Yasufumi  東京工業大学, 大学院理工学研究科, 助教 (90581596)
Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywordsテスト配位列 / K-安定性 / Donaldson-二木不変量 / polybalanced計量 / 相対安定性 / 偏極代数多様体
Outline of Final Research Achievements

We made a systematic study of the completion of the moduli space of test configurations for a polarized algebraic mamifold. As a typical example of our study, we obtain the Donaldson-Futaki invariant for sequences of test configurations on a polarized algebraic manifold. This then allows us to introduce the concept of strong K-stability. Moreover, by a joint work with Nitta, we showed that strong K-stability implies asymptotic Chow stability. These results in particular give us various applications in the existence problem of extremal Kaehler metrics.

Report

(5 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (13 results)

All 2016 2015 2014 2013

All Journal Article (7 results) (of which Peer Reviewed: 7 results,  Open Access: 1 results) Presentation (6 results) (of which Int'l Joint Research: 2 results,  Invited: 6 results)

  • [Journal Article] The Yau-Tian-Donaldson conjecture for general polarizations, I2016

    • Author(s)
      T. Mabuchi
    • Journal Title

      Springer Proc. Math. Stat.

      Volume: 154 Pages: 235-245

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An l-th root of a test configuration of exponent l2016

    • Author(s)
      T. Mabuchi
    • Journal Title

      Complex Manifolds

      Volume: 3 Issue: 1 Pages: 169-185

    • DOI

      10.1515/coma-2016-0005

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] The Yau-Tian-Donaldson conjecture for general polarizations, I2016

    • Author(s)
      T. Mabuchi
    • Journal Title

      Geometry and Topology of Manifolds, Springer Japan

      Volume: 1

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] The Donaldson-Futaki invariant for sequences of test configurations2015

    • Author(s)
      T. Mabuchi
    • Journal Title

      Progress in Math., Birkh\"auser

      Volume: 308 Pages: 395-403

    • Related Report
      2015 Research-status Report 2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Strong K-stability and asymptotic Chow-stability2015

    • Author(s)
      T. Mabuchi and Y. Nitta
    • Journal Title

      Progress in Math., Birkh\"auser

      Volume: 308 Pages: 405-411

    • Related Report
      2015 Research-status Report 2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Relative stability and extremal metrics2014

    • Author(s)
      T. Mabuchi
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 66 Issue: 2 Pages: 535-563

    • DOI

      10.2969/jmsj/06620535

    • NAID

      130003394369

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2014 Research-status Report 2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] NEW EXAMPLES OF SASAKI-EINSTEIN MANIFOLDS2013

    • Author(s)
      T.Mabuchi and Y.Nakagawa
    • Journal Title

      Tohoku Mathematical Journal, Second Series

      Volume: 65 Issue: 2 Pages: 243-252

    • DOI

      10.2748/tmj/1372182724

    • NAID

      130005562143

    • ISSN
      0040-8735, 2186-585X
    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Polybalanced metrics associated to extremal Kaehler metrics2016

    • Author(s)
      T. Mabuchi
    • Organizer
      Complex Geometry Conference (in honor of Prof. Mok's 60th birthday)
    • Place of Presentation
      KIAS, Seoul
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Strong K-stability for general polarizations2015

    • Author(s)
      T. Mabuchi
    • Organizer
      Recent Advances in K\"ahler Geometry
    • Place of Presentation
      Vanderbilt University
    • Year and Date
      2015-05-19
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] K-stability and strong K-stability2014

    • Author(s)
      T. Mabuchi
    • Organizer
      Complex Geometry and Algebraic Geometry
    • Place of Presentation
      Beijing International Center for Mathematical Research
    • Year and Date
      2014-07-14
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Donaldson-Tian-Yau's conjecture for general polarization2013

    • Author(s)
      T. Mabuchi
    • Organizer
      Ricci curvature: limit spaces and Kaehler geometry
    • Place of Presentation
      ICMS, Edinburgh
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] The Donaldson-Tian-Yau conjecture for extremal metrics2013

    • Author(s)
      T. Mabuchi
    • Organizer
      The Asian Mathematical Conference 2013
    • Place of Presentation
      BEXCO, Busan, Korea
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] A new version of the Donaldson-Tian-Yau conjecture for extremal metrics2013

    • Author(s)
      T. Mabuchi
    • Organizer
      Workshop "Extremal Kaehler metrics"
    • Place of Presentation
      CRM, Montreal, Canada
    • Related Report
      2013 Research-status Report
    • Invited

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Published: 2014-07-25   Modified: 2019-07-29  

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