Improvement of the foundation of Hodge modules and their further applications

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540039
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: Saito Morihiko 京都大学, 数理解析研究所, 准教授 (10186968)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: ホッジ加群 / 半正定値性定理 / 許容法関数 / b-関数 / 超平面配置 / ヒルツェブルフ類 / コンツェヴィチ複体 / フロベニウス多様体

Outline of Final Research Achievements

We studied a better definition of mixed Hodge modules, and got many new results in various fields of algebraic geometry such as algebraic cycles, singularities, Hodge structures, characteristic classes, and so on by applying the theory of mixed Hodge modules. For instance, the roots of the b-functions of certain homogeneous polynomials can be determined by calculating the Hilbert series of the quotient ring of the polynomial ring divided by the Jacobian ideal generated by the partial derivatives of the given polynomial. This is totally impossible without using the theory of mixed Hodge modules.

Free Research Field

代数幾何学