New applications of the theory of Hodge modules to algebraic geometry

2008 Fiscal Year Final Research Report

• Project/Area Number: 19540023
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: SAITO Morihiko Kyoto University, 数理解析研究所, 准教授 (10186968)
• Project Period (FY): 2007 – 2008
• Keywords: ホッジ加群 / ネロン模型 / 認容法函数 / スペクトラム / 消滅輪体 / チャウ・キュネット分解 / 交叉コホモロジー / 超平面配置

Research Abstract

代数幾何学の基礎の一つであるホッジ加群の理論とは, グロタンディック・ドリーニュらによってヴェイユ予想の解決の為に創られた理論に標数0の世界において対応する物として元来発見されたのであるが、その応用については基本的なものを除いては未だ十分に研究され尽くされているとは言えない状態にある。そこでホッジ加群の応用について研究を行い、それがネロン模型の一般化やチャウ・キュネット分解等の研究に有効である事を示した。

Research Products

• [Journal Article] Lowest Weights in Cohomology of Variations of Hodge Structure, to appear in Nagoya Math
  • Author(s): Chris Peters, Morihiko Saito
  • Journal Title: Journal
  • Peer Reviewed
• [Journal Article] Relative Chow-Kunneth decompositions for conic bundles and Prym varieties, to appear in Intern
  • Author(s): Jan Nagel, Morihiko Saito
  • Journal Title: Math. Research Notices
  • Peer Reviewed
• [Journal Article] On b-function
  • Author(s): Morihiko Saito
  • Journal Title: spectrum and multiplier ideals, to appear in Advanced Studies in Pure Mathematics
  • Peer Reviewed
• [Presentation] Cycles evanescents d'une fonction dont la fibre generique est lisse (2008)
  • Author(s): Morihiko Saito
  • Organizer: Singularites et applications
  • Place of Presentation: Nice, France
  • Year and Date: 2008-11-07
• [Presentation] Conjecture de Hodge et cycles evanescents (2008)
  • Author(s): Morihiko Saito
  • Organizer: Singularites et applications
  • Place of Presentation: Nice, France
  • Year and Date: 2008-11-07
• [Presentation] Hausdorff property of the Zucker extension (2008)
  • Author(s): Morihiko Saito
  • Organizer: Hodge Theory
  • Place of Presentation: Banff, Canada
  • Year and Date: 2008-04-07
• [Presentation] Sur la b-fonction, le spectre et les ideaux multiplicateurs d'une function (2007)
  • Author(s): Morihiko Saito
  • Organizer: Singularites et geometrie complexes
  • Place of Presentation: University of Nancy, France
  • Year and Date: 2007-09-06
• [Presentation] On b-function, spectrum, and multiplier ideals (2007)
  • Author(s): Morihiko Saito
  • Organizer: Niigata Workshop on Complex Geometry and Singularities
  • Place of Presentation: 新潟
  • Year and Date: 2007-08-22
• [Presentation] On b-function, spectrum, and multiplier ideals (2007)
  • Author(s): Morihiko Saito
  • Organizer: Algebraic Analysis and Around in honor of Professor Masaki Kashiwara's 60th birthday
  • Place of Presentation: RIMS京都
  • Year and Date: 2007-06-28
• [Presentation] Spectrum, b-function, and multiplier ideals (2007)
  • Author(s): Morihiko Saito
  • Organizer: Geometry Days In honour of Joseph Steenbrink on his 60th birthday
  • Place of Presentation: Radboud University, Nijmegen, Netherlands
  • Year and Date: 2007-06-02