On Lagrangian fibratins of symplectic varieties

• Project/Area Number: 21684001
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Hokkaido University
• Principal Investigator: MATSUSHITA Daisuke 北海道大学, 大学院・理学研究院, 准教授 (90333591)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥7,540,000 (Direct Cost: ¥5,800,000、Indirect Cost: ¥1,740,000); Fiscal Year 2012: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: シンプレクティック / ラグランジアン

Research Abstract

We show that the base space of a Lagrangian fibration is a projective space if the source symplectic variety satisfies certain numerical conditions. We obtain the necessary and sufficient condition of existence of a Lagrangian fibration for all known examples. We also show smoothness of components of the relative moduli space of aLagrangian fibration which parametrize invertible sheaves on each fibre.

Research Products

• [Journal Article] On Lagrangian fibrations (2013)
  • Author(s): 松下大介
  • Journal Title: 第57回代数学シンポジウム報告集 Volume: vol57 Pages: 177-182
• [Journal Article] On Lagrangian fibrations (2013)
  • Author(s): 松下大介
  • Journal Title: 第５７回代数学シンポジウム報告集 Volume: 57 Pages: 177-182
• [Presentation] A base space of Lagrangian fibrations of symplectic varieties (2013)
  • Author(s): Daisuke MATSUSHITA
  • Organizer: Laboratory of algebraic geometry: weekly seminar(招待講演)
  • Place of Presentation: Russia, Moscow, Higher School of Economy.
  • Year and Date: 2013-03-06
• [Presentation] A base space of Lagrangian fibrations of symplectic varieties (2013)
  • Author(s): Daisuke MATSUSHITA
  • Organizer: Laboratory of algebraic geometry: weekly seminar
  • Place of Presentation: Russia, Moscow, Higher School of Economy
  • Invited
• [Presentation] On birational semi-rigidity of Lagrangian fibrations (2012)
  • Author(s): 松下大介
  • Organizer: 大阪大学代数幾何セミナー(招待講演)
  • Place of Presentation: 大阪大学(大阪府豊中市)
  • Year and Date: 2012-12-17
• [Presentation] On isotropic divisors of the Hilbert scheme of K3 surfaces (2012)
  • Author(s): Daisuke MATSUSHITA
  • Organizer: Hyper-Kahler Geometry(招待講演)
  • Place of Presentation: USA, NY, Simons Center of Geometry.
  • Year and Date: 2012-11-01
• [Presentation] On Lagrangian fibrations (2012)
  • Author(s): 松下大介
  • Organizer: 第57回代数学シンポジウム(招待講演)
  • Place of Presentation: 京都大学数理解析研究所(京都市左京区)
  • Year and Date: 2012-08-22
• [Presentation] On semiampleness of nef divisors on the hilbert scheme of K3 surfaces (2012)
  • Author(s): Daisuke MATSUSHITA
  • Organizer: Kaehler geometry builds on classical algebraic geometry(招待講演)
  • Place of Presentation: フランス,ナント,Leray研究所
  • Year and Date: 2012-05-24
• [Presentation] Birational semi rigidity of Lagrangian fibrations (2012)
  • Author(s): Daisuke MATSUSHITA
  • Organizer: Symposium on projective algebraic varieties and moduli(招待講演)
  • Place of Presentation: 韓国,プサン,Novotel hotel.
  • Year and Date: 2012-02-16
• [Presentation] Birational semi rigidity of Lagrangian fibrations (2012)
  • Author(s): 松下大介
  • Organizer: Symposium on Projective Algebraic Varieties and Moduli
  • Place of Presentation: Novotel, Busan(韓国)(招待講演)
  • Year and Date: 2012-02-16
• [Presentation] On semiampleness of nef divisors on the hilbert scheme of K3 surfaces (2012)
  • Author(s): Daisuke MATSUSHITA
  • Organizer: Kaehler geometry builds on classical algebraic geometry
  • Place of Presentation: フランス, ナント, Leray研究所
  • Invited
• [Presentation] On Lagrangian fibrations (2012)
  • Author(s): 松下大介
  • Organizer: 第５７回代数学シンポジウム
  • Place of Presentation: 京都大学数理解析研究所(京都市左京区)
  • Invited
• [Presentation] On isotropic divisors of the Hilbert scheme of K3 surfaces (2012)
  • Author(s): Daisuke MATSUSHITA
  • Organizer: Hyper-Kahler Geometry
  • Place of Presentation: USA, NY, Simons Center of Geometry
  • Invited
• [Presentation] On birational semi-rigidity of Lagrangian fibrations (2012)
  • Author(s): 松下大介
  • Organizer: 大阪大学代数幾何セミナー
  • Place of Presentation: 大阪大学(大阪府豊中市)
  • Invited
• [Presentation] On rational Lagrangian fibrations of irreducible symplectic manifolds (2011)
  • Author(s): Daisuke MATSUSHITA
  • Organizer: Moduli spaces and automorphic forms(招待講演)
  • Place of Presentation: フランス, マルセイユ, Luminy 研究所.
  • Year and Date: 2011-10-14
• [Presentation] On rational Lagrangian brations of irreducible symplectic Manifolds (2011)
  • Author(s): 松下大介
  • Organizer: Moduli spaces and automorphic forms
  • Place of Presentation: Centre International de Rencontres Mathematiques(フランス)(招待講演)
  • Year and Date: 2011-10-14
• [Presentation] 単位円板上のAbelianfibrationの双対極小モデルについて (2010)
  • Author(s): 松下大介
  • Organizer: 京都大学代数幾何セミナー(招待講演)
  • Place of Presentation: 京都大学(京都市左京区)
  • Year and Date: 2010-05-21
• [Presentation] 単位円上のAbelian fibrationの相対極小モデルについて (2010)
  • Author(s): 松下大介
  • Organizer: 代数幾何学セミナー
  • Place of Presentation: 京都大学(京都市)(招待講演)
  • Year and Date: 2010-05-21
• [Presentation] On Lagrangian fibrations (2010)
  • Author(s): Daisuke MATSUSHITA
  • Organizer: Algebraic Geometry Seminar(招待講演)
  • Place of Presentation: USA, Ann Arbor, University of Michigan.
  • Year and Date: 2010-02-10
• [Presentation] On Lagrangian fibrations (2010)
  • Author(s): 松下大介
  • Organizer: Algebraic Geometry Seminar
  • Place of Presentation: University of Michigan
  • Year and Date: 2010-02-10
• [Presentation] アーベル多様体の相対コンパクト化について (2009)
  • Author(s): 松下大介
  • Organizer: 代数幾何の諸問題
  • Place of Presentation: 北海道大学(札幌市北区)
  • Year and Date: 2009-09-02
• [Presentation] アーベル多様体の相対コンパクト化について (2009)
  • Author(s): 松下大介
  • Organizer: 代数幾何の諸問題
  • Place of Presentation: 北海道大学
  • Year and Date: 2009-09-02
• [Presentation] On elliptic fibrations and Lagrangian fibrations (2009)
  • Author(s): 松下大介
  • Organizer: 京都大学談話会(招待講演)
  • Place of Presentation: 京都大学(京都市左京区)
  • Year and Date: 2009-06-24
• [Presentation] On elliptic fibrations and Lagrangian fibrations (2009)
  • Author(s): 松下大介
  • Organizer: 京都大学談話会
  • Place of Presentation: 京都大学
  • Year and Date: 2009-06-24