• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Research on pluricanonical bundles and multiplier ideal sheaves for a degenerate family of complex manifolds

Research Project

Project/Area Number 19340014
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

TAKAYAMA Shigeharu  東京大学, 大学院・数理科学研究科, 准教授 (20284333)

Co-Investigator(Kenkyū-buntansha) 平地 健吾  東京大学, 大学院・数理科学研究科, 准教授 (60218790)
今野 宏  東京大学, 大学院・数理科学研究科, 准教授 (20254138)
大沢 健夫  名古屋大学, 大学院・多元数理科学研究科, 教授 (30115802)
満渕 俊樹  大阪大学, 大学院・理学研究科, 教授 (80116102)
佐藤 栄一  九州大学, 大学院・数理科学研究院, 教授 (10112278)
Co-Investigator(Renkei-kenkyūsha) HIRACHI Kengo  東京大学, 大学院・数理科学研究科, 教授 (60218790)
KONNO Rihoshi  東京大学, 大学院・数理科学研究科, 准教授 (20254138)
TAKAGI Shunsuke  東京大学, 大学院・数理科学研究科, 准教授 (40380670)
OHSAWA Takeo  名古屋大学, 大学院・多元数理科学研究科, 教授 (30115802)
MABIUCHI Toshiki (SATO Eiichi)  大阪大学, 大学院・理学研究科, 教授 (10112278)
HAYASHIMOTO Atsushi  国立長野高専, 一般科, 准教授 (90342493)
Research Collaborator MOUROUGANE Christophe  フランスレンヌ大学, 教授
Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥11,440,000 (Direct Cost: ¥8,800,000、Indirect Cost: ¥2,640,000)
Fiscal Year 2010: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2009: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2008: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2007: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Keywords多重標準束 / 乗数イデアル層 / 退化族 / ホッジ計量 / 幾何学
Research Abstract

For a smooth proper Kaehler morphism f : X→Y and a Nakano semi-positive vector bundle(E, h) on X, we showed that every direct image sheaf R^qf_* K_{ X/Y}(E) is locally free and that it is equipped with a natural Hermitian metric, called a Hodge metric, with Nakano semi-positive curvature. Moreover even when f : X→Y can be singular, we showed that the positivity of a direct image sheaf extends across the singular locus of f on Y.

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

    (42 results)

All 2011 2010 2009 2008 2007 Other

All Journal Article (24 results) (of which Peer Reviewed: 23 results) Presentation (16 results) Remarks (2 results)

  • [Journal Article] 複素幾何学の諸問題2011

    • Author(s)
      高山茂晴
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 第1731巻 Pages: 198-198

    • Related Report
      2010 Final Research Report
  • [Journal Article] Adjoint ideals along closed subvarieties of higher codimension2010

    • Author(s)
      Takagi S.
    • Journal Title

      J. Reine Angew. Math

      Volume: 641 Pages: 145-162

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A tower of Riemann surfaces whose Bergman kernels jump at the roof2010

    • Author(s)
      Ohsawa T.
    • Journal Title

      Publ. Res. Inst. Math. Sci

      Volume: 46 Pages: 473-478

    • NAID

      110007697225

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Extension of twisted Hodge metrics for Kaehler morphisms2009

    • Author(s)
      Mourougane Ch. Takayama S.
    • Journal Title

      J. Differential Geom.

      Volume: 83 Pages: 131-161

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A remark on Kazhdan's theorem on sequences of Bergman metrics2009

    • Author(s)
      Ohsawa T.
    • Journal Title

      Kyushu J. Math

      Volume: 63 Pages: 133-137

    • NAID

      130000135275

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds2009

    • Author(s)
      Mabuchi T.
    • Journal Title

      Osaka J. Math

      Volume: 46 Pages: 115-139

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Multigraded rings, diagonal subalgebras, and rational singularities2009

    • Author(s)
      Kurano K., Sato E., Anurag S. and Watanabe K.
    • Journal Title

      J. Algebra

      Volume: 322 Pages: 3248-3267

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Extension of twisted Hodge metrics for Kaehler morphisms2009

    • Author(s)
      Mourougane Ch.-Takayama S.
    • Journal Title

      J.Differential Geom. 83

      Pages: 131-161

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Extension of twisted Hodge metrics for Kaehler morphisms2009

    • Author(s)
      高山茂晴-Mourougane Ch.
    • Journal Title

      J.Differential Geom. 83

      Pages: 131-161

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hodge metrics and the curvature of higher direct images2008

    • Author(s)
      Mourougane Ch. and Takayama S.
    • Journal Title

      Ann. Sci. Ecole Norm. Sup.

      Volume: 41 Pages: 905-924

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On uniruled degenerations of algebraic varieties with trivial canonical divisor2008

    • Author(s)
      Takayama S.
    • Journal Title

      Math. Z.

      Volume: 259 Pages: 487-501

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the uniruledness of stable base loci2008

    • Author(s)
      Takayama S.
    • Journal Title

      J. Differential Geom.

      Volume: 78 Pages: 521-541

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A characteristic p analogue of plt singularities and adjoint ideals2008

    • Author(s)
      Takagi S.
    • Journal Title

      Math. Z

      Volume: 259 Pages: 321-341

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Chow-stability and Hilbert-stability in Mumford's geometric invariant theory2008

    • Author(s)
      Mabuchi T.
    • Journal Title

      Osaka J. Math

      Volume: 45 Pages: 833-846

    • NAID

      120004841938

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hyperplane section principle of Lefschetz on conic-bundle and blowing-down2008

    • Author(s)
      Sato E.
    • Journal Title

      Kodai Math. J

      Volume: 31 Pages: 307-322

    • NAID

      130004687892

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hodge metrics and the curvature of higher direct images2008

    • Author(s)
      Mourougane Ch.\-Takayama S.
    • Journal Title

      Ann.Sci.Ecole Norm.Sup. 41

      Pages: 905-924

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On uniruled degenerations of algebraic varieties with trivial canonical divisor2008

    • Author(s)
      Takayama S.
    • Journal Title

      Math.Z. 259

      Pages: 487-501

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On the uniruledness of stable base loci2008

    • Author(s)
      Takayama S.
    • Journal Title

      J.Differential Geom. 78

      Pages: 521-541

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On the uniruledness of stable base loci2008

    • Author(s)
      高山茂晴
    • Journal Title

      J. Differential Geom. 78

      Pages: 521-541

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On uniruled degenerations of algebraic varieties with trivial canonical divisor2008

    • Author(s)
      高山茂晴
    • Journal Title

      Math. Z. 259

      Pages: 487-501

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hodge metrics and the curvature of higher direct images2008

    • Author(s)
      高山茂晴-Mourougane Ch.
    • Journal Title

      Ann. Sci. Ecole Norm. Sup. 41

      Pages: 905-924

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hodge metrics and positivity of direct images2007

    • Author(s)
      高山 茂晴-Mourougane Ch,
    • Journal Title

      J.ReineAngew.Math. 606

      Pages: 167-178

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the invariance and the lower semi-continuity of plurigenera of algebraic varieties2007

    • Author(s)
      高山 茂晴
    • Journal Title

      J.Algebraic Geom 16

      Pages: 1-18

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A remark on pseudoconvex domains with analytic complements in compact Kahler manifolds2007

    • Author(s)
      大沢 健夫
    • Journal Title

      J.Math.Kyoto Univ 47

      Pages: 115-119

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Kaehler-Einstein幾何の問題、複素幾何学の諸問題2010

    • Author(s)
      満渕俊樹
    • Place of Presentation
      京大数理研
    • Year and Date
      2010-09-09
    • Related Report
      2010 Final Research Report
  • [Presentation] CR幾何の問題、複素幾何学の諸問題2010

    • Author(s)
      平地健吾
    • Place of Presentation
      京大数理研
    • Year and Date
      2010-09-08
    • Related Report
      2010 Final Research Report
  • [Presentation] Bergman核の問題、複素幾何学の諸問題2010

    • Author(s)
      大沢健夫
    • Place of Presentation
      京大数理研
    • Year and Date
      2010-09-07
    • Related Report
      2010 Final Research Report
  • [Presentation] Hodge metrics and the curvature of higher direct image sheaves2010

    • Author(s)
      高山茂晴
    • Organizer
      ICM2010 satellite conference "Complex Geometry, Group Actions and Moduli Spaces"
    • Place of Presentation
      Hyderabad, India
    • Year and Date
      2010-08-14
    • Related Report
      2010 Final Research Report
  • [Presentation] Hodge metrics and the curvature of higher direct image sheaves2010

    • Author(s)
      高山茂晴
    • Organizer
      Complex Geometry, Group Actions and Moduli Spaces
    • Place of Presentation
      Hyderabad, India
    • Year and Date
      2010-08-14
    • Related Report
      2010 Annual Research Report
  • [Presentation] 高次順像層のホッジ計量について2009

    • Author(s)
      高山茂晴
    • Organizer
      日本数学会、函数論分科会
    • Place of Presentation
      東大
    • Year and Date
      2009-03-29
    • Related Report
      2010 Final Research Report
  • [Presentation] 高次順像層のホッジ計量について2009

    • Author(s)
      高山茂晴
    • Organizer
      日本数学会 函数論分科会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-29
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] 高次順像層のホッジ計量について2009

    • Author(s)
      高山茂晴
    • Organizer
      日本数学会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-29
    • Related Report
      2008 Annual Research Report
  • [Presentation] L^2-extendability from analytic subsets with singularities2009

    • Author(s)
      大沢健夫
    • Organizer
      Complex Geometry Workshop 2009 Tokyo
    • Place of Presentation
      東大
    • Year and Date
      2009-02-13
    • Related Report
      2010 Final Research Report
  • [Presentation] On the extension of twisted Hodge metrics2008

    • Author(s)
      高山茂晴
    • Organizer
      複素幾何学シンポジウム
    • Place of Presentation
      長野県真田町
    • Year and Date
      2008-10-23
    • Related Report
      2010 Final Research Report
  • [Presentation] 多重標準形式の拡張とその応用2008

    • Author(s)
      高山茂晴
    • Organizer
      代数学シンポジウム
    • Place of Presentation
      盛岡市
    • Year and Date
      2008-08-06
    • Related Report
      2010 Final Research Report
  • [Presentation] ホッジ計量の拡張について、Bergman核と代数幾何への応用2008

    • Author(s)
      高山茂晴
    • Place of Presentation
      京大数理研
    • Year and Date
      2008-06-04
    • Related Report
      2010 Final Research Report
  • [Presentation] Boundednedd of pluricanonical systems on algebraic varieties of general type2007

    • Author(s)
      高山茂晴
    • Organizer
      Algebraic Geometry and Commutative Algebra Tokyo 2007
    • Place of Presentation
      東大
    • Year and Date
      2007-12-12
    • Related Report
      2010 Final Research Report
  • [Presentation] Hodge metrics and the curvature of higher direct images2007

    • Author(s)
      高山茂晴
    • Organizer
      Complex geometry in Osaka
    • Place of Presentation
      阪大
    • Year and Date
      2007-11-02
    • Related Report
      2010 Final Research Report
  • [Presentation] Boundednedd of pluricanonical systems on algebraic varieties of general type2007

    • Author(s)
      高山茂晴
    • Organizer
      Algebraic and Arithmetic Structures of Moduli Spaces
    • Place of Presentation
      北大
    • Year and Date
      2007-09-04
    • Related Report
      2010 Final Research Report
  • [Presentation] Boundedness of pluricanonical systems on algebraic varieties of general type2007

    • Author(s)
      高山 茂晴
    • Organizer
      Algebraic and Arithmetic Structures of Moduli Spaces
    • Place of Presentation
      札幌、北大
    • Year and Date
      2007-09-04
    • Related Report
      2007 Annual Research Report
  • [Remarks]

    • URL

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

    • Related Report
      2010 Final Research Report
  • [Remarks] ホームページ

    • URL

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

    • Related Report
      2009 Self-evaluation Report

URL: 

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

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi