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On constructing of a minimal model of fibred algebraic varieties whose Kodaira dimension is zero

Research Project

Project/Area Number 23654002
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionHokkaido University

Principal Investigator

MATSUSHITA Daisuke  北海道大学, 理学(系)研究科(研究院), 准教授 (90333591)

Co-Investigator(Renkei-kenkyūsha) FUJINO Osamu  京都大学, 大学院・理学研究科, 准教授 (60324711)
KAWAKITA Masayuki  京都大学, 数理解析研究所, 准教授 (10378961)
TAKAGI Hiromichi  東京大学, 大学院・数理科学研究科, 准教授 (30322150)
Project Period (FY) 2011 – 2012
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords極小モデル / アーベル多様体 / ラグランジアン / シンプレクティック / 小平次元 / ファイブレーション
Research Abstract

Let us consider a smooth abelian fibration over a punctured disk or an open set of polydisk which obtained by removing a hypersurface. It is natural question whether these families can be extended over a disk or a polydisk. On 80th, it was announced that we could obtain such a relative compactification with a incomplete proof. Since semidarkness of the proof, there are several results with technical assumptions. By this result, we may get rid of these assumptions and obtain idealistic results.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (17 results)

All 2014 2013 2012 2011 Other

All Journal Article (4 results) (of which Peer Reviewed: 4 results) Presentation (13 results) (of which Invited: 13 results)

  • [Journal Article] On almost holomorphic Lagrangian fibrations2014

    • Author(s)
      Daisuke MATSUSHITA
    • Journal Title

      Math. Ann

      Volume: vol.357 Pages: 565-57

    • NAID

      120005600745

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On almost holomorphic Lagrangian fibrations2014

    • Author(s)
      Daisuke MATSUSHITA
    • Journal Title

      Math. Ann.

      Volume: 358 Issue: 3-4 Pages: 565-572

    • DOI

      10.1007/s00208-013-0964-8

    • NAID

      120005600745

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Zariski decomposition and Lagrangian fibration on HyperKahler manifolds2013

    • Author(s)
      Daisuke MATSUSHITA and De-Qi Zhang
    • Journal Title

      Math. Res. Lett

      Volume: Vol.5 Pages: 1-9

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Zariski decomposition and Lagrangian fibration on HyperKahler manifolds2013

    • Author(s)
      Daisuke MATSUSHITA, De-Qi Zhang
    • Journal Title

      Math. Res. Lett.

      Volume: 5 Pages: 1-9

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Presentation] On the dual fibration of a Lagrangian fibration2014

    • Author(s)
      Daisuke MATSUSHITA
    • Organizer
      Moduli spaces of irreducible symplectic varieties, cubics and Enriques surfaces
    • Place of Presentation
      Laboratoire Paul Paneleve,フランス
    • Year and Date
      2014-03-28
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] "On base manifolds of Lagrangian fibration of singular symplectic manifolds", Symplectic Algebraic Geometry2013

    • Author(s)
      Daisuke MATSUSHITA
    • Organizer
      関西セミナーハウス
    • Place of Presentation
      京都府
    • Year and Date
      2013-10-04
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] "A base space of Lagrangian fibrations of symplectic varieties", Laboratory of algebraic geometry2013

    • Author(s)
      Daisuke MATSUSHITA
    • Organizer
      weekly seminar
    • Place of Presentation
      Higher school of Economy, ロシア
    • Year and Date
      2013-03-06
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] On birational semi-rigidityof Lagrangian fibration2012

    • Author(s)
      Daisuke MATSUSHITA
    • Organizer
      大阪大学代数幾何セミナー
    • Place of Presentation
      大阪大学, 豊中市
    • Year and Date
      2012-12-17
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] On isotropic divisors of the Hilbert scheme of K3 surfaces2012

    • Author(s)
      Daisuke MATSUSHITA
    • Organizer
      Hyper Kaehler Geometry, Simons Center for Geometry and Physics
    • Place of Presentation
      アメリカ
    • Year and Date
      2012-11-01
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] On Lagrangian fibations2012

    • Author(s)
      Daisuke MATSUSHITA
    • Organizer
      代数学シンポジウム
    • Place of Presentation
      京都大学, 京都市
    • Year and Date
      2012-08-22
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] On semiampleness of nef divisorson the Hilbert scheme of K3 surfaces2012

    • Author(s)
      Daisuke MATSUSHITA
    • Organizer
      Geometry of Kaehler manifolds
    • Place of Presentation
      Jean Leray Institute of Mathematics, フランス
    • Year and Date
      2012-05-24
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Birational semi rigidity of Lagrangian fibrations2012

    • Author(s)
      Daisuke MATSUSHITA
    • Organizer
      Symposium on Projective Algebraic Varieties and Moduli
    • Place of Presentation
      Novotel Busan Ambassador, 韓国
    • Year and Date
      2012-02-16
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] On birational semi-rigidity of Lagrangian fibrations2012

    • Author(s)
      松下大介
    • Organizer
      大阪大学代数幾何学セミナー
    • Place of Presentation
      大阪大学(大阪府豊中市)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] On rational Lagrangian fibrations of irreducible symplectic Manifolds2011

    • Author(s)
      Daisuke MATSUSHITA
    • Organizer
      Moduli spaces and automorphic forms
    • Place of Presentation
      Centre International de Recontre Mathematique, フランス
    • Year and Date
      2011-10-14
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] On base manifolds of Lagrangian fibrations

    • Author(s)
      松下大介
    • Organizer
      代数多様体のトポロジーとその周辺
    • Place of Presentation
      札幌, 北海道大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On base manifolds of Lagrangian fibration of singular symplectic manifolds

    • Author(s)
      Daisuke MATSUSHITA
    • Organizer
      Symplectic Algebraic Geometry
    • Place of Presentation
      京都, 関西セミナーハウス
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On the dual fibration of a Lagrangian fibration

    • Author(s)
      Daisuke MATSUSHITA
    • Organizer
      Moduli spaces Lille 2014
    • Place of Presentation
      Lille France
    • Related Report
      2013 Annual Research Report
    • Invited

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Published: 2011-08-05   Modified: 2019-07-29  

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