On the structures of Lagrangian fibrations

2008 Fiscal Year Final Research Report

• Project/Area Number: 18684001
• 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 Hokkaido University, 大学院理学研究院, 准教授 (90333591)
• Project Period (FY): 2006 – 2008
• Keywords: シンプレクティック / ラグランジアン

Research Abstract

シンプレクティック多様体に入るラグランジアンファイブレーションについて, 特異ファイバーの構造を決定した。またラグランジアンファイブレーションを保ったまま変形出来るシンプレクティック多様体がそのモジュライ空間の中で余次元1の族をなすことを示した。さらにシンプレクティック多様体の双有理的な特質の一つを見出した。

Research Products

• [Journal Article] On nef reductions of projective irreducible symplectic manifolds (2008)
  • Author(s): Matsushita D
  • Journal Title: Math. Z vol. 258, no. 2 Pages: 267-270
  • Peer Reviewed
• [Presentation] On Lagrangian fibrations (2009)
  • Author(s): Matsushita, D
  • Organizer: 第四回代数・解析・幾何セミナー
  • Place of Presentation: 鹿児島大学
  • Year and Date: 2009-02-19
• [Presentation] Toward deformations of Lagrangian fibrations on symplectic varieties (2008)
  • Author(s): Matsushita, D
  • Organizer: Algebraic Geometry in East Asia, Korean Institute for Advanced Study
  • Place of Presentation: Korea
  • Year and Date: 2008-11-13
• [Presentation] On deformations of Lagrangian fibrations (2008)
  • Author(s): Matsushtia, D
  • Organizer: 代数幾何学シンポジューム
  • Place of Presentation: 城崎大会議館
  • Year and Date: 2008-10-21
• [Presentation] On deformations of Lagrangian fibrations, moduli 空間と双有理幾何学 (2008)
  • Author(s): Matsushita, D
  • Organizer: 京都大学数理解析研究所
  • Year and Date: 2008-06-18
• [Presentation] Applications of flops on symplectic manifolds (2008)
  • Author(s): Matsushita, D
  • Organizer: Mathematics seminar, Korean Institute for Advanced Study
  • Place of Presentation: Korea
  • Year and Date: 2008-03-25
• [Presentation] On symplectic resolution of an isolated singularity (2) (2008)
  • Author(s): Matsushita, D
  • Organizer: Mathematics seminar, Korean Institute for Advanced Study
  • Place of Presentation: Korea
  • Year and Date: 2008-03-12
• [Presentation] On symplectic resolution of an isolated singularity (1) (2008)
  • Author(s): Matsusihta, D
  • Organizer: Mathematics seminar, Korean Institute for Advanced Study
  • Place of Presentation: Korea
  • Year and Date: 2008-03-05
• [Presentation] On remarks of teminations of D-flops on symplectic manifolds (2008)
  • Author(s): Matsushita, D
  • Organizer: UK-Japan Winter School
  • Place of Presentation: University of Warwick, England
  • Year and Date: 2008-01-10
• [Presentation] On singular fibres of Lagrangian fibrations, ベクトル束と高次元代数多様体 (2007)
  • Author(s): Matsushita, D
  • Organizer: 京都大学数理解析研究所
  • Year and Date: 2007-07-06
• [Presentation] On base point freenes, Seminar on algebraic geometry (2006)
  • Author(s): Matsushita. D
  • Organizer: Max- Plank-Institute
  • Place of Presentation: Germany
  • Year and Date: 2006-06-07
• [Presentation] On existence conditions of Lagrangian fibrations (2006)
  • Author(s): Matsushita, D
  • Organizer: Workshop on holomophic symplectic varieties, Max-Plank-Institute
  • Place of Presentation: Germany
  • Year and Date: 2006-05-24
• [Presentation] On Lagrangian abelian subvariety of symplectic manifolds (2006)
  • Author(s): Matsushita, D
  • Organizer: 代数幾何ミニワークショップ
  • Place of Presentation: 東京大学
  • Year and Date: 2006-04-11
• [Remarks] D.Matsushita, A canonical bundle formula for projective Lagrangian fibrations, ArXiv: 0710.0122
• [Remarks] D.Matsushita, On deformation of Lagrangian fibrations, ArXiv : 0903.2098