New applications of the theory of mixed Hodge modules and mixed sheaves
| Project/Area Number |
21540037
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
SAITO Morihiko 京都大学, 数理解析研究所, 准教授 (10186968)
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| Project Period (FY) |
2009 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | ホッジ加群 / ネロン模型 / チャウ・キュネット分解 / 超平面配置 / ヒルツェブルフ類 / 消滅輪体 / コンツェヴィチ予想 / コンツェビッチ予想 / ミルナー類 / 混合ホッジ加群 / 局所モノドロミー / 対称積 / ヒルツェブルフ特性類 / 仮想特性類 / 双対加群 / ホッジ予想 / 許容法函数 / 柏原予想 / 非確定型微分方程式系 |
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| Research Abstract |
By applying the theory of mixed Hodge modules, many new results are obtained in various fields of algebraic geometry such as Hodge structures, algebraic cycles, singularities, characteristic classes, etc. In case of characteristic classes, for instance, a completely new formula for the Hirzebruch-Milnor classes of complete intersections of smooth projective varieties is obtained by using vanishing cycles of mixed Hodge modules inductively. Many of these results cannot be proved without using the theory of mixed Hodge modules.
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Report
(4 results)
Research Products
(10 results)
