Singular Chern Class and Enumerative Geometry
| Project/Area Number |
21540057
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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 |
Geometry
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| Research Institution | Hokkaido University |
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Principal Investigator |
OHMOTO Toru 北海道大学, 大学院・理学研究院, 准教授 (20264400)
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| Co-Investigator(Kenkyū-buntansha) |
秦泉寺 雅夫 北海道大学, 大学院・理学研究院, 准教授 (20322795)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 特異点論 / 特性類 / 特異チャーン類 / トム多項式 / 特異点 / Chern-Schwartz-MacPherson class / Hirzebruch class / Hilbert scheme / Symmetric product / 国際研究者交流 / 米国:ドイツ / 特異多様体 / 代数的スタック / チャーン・マクファーソン自然変換 / 構成的関数 / トム・マザー理論 / ヴァシリエフ不変量 |
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| Research Abstract |
In this grant project, I developed in two directions my previous researches on the theory of equivariant singular Chern class. The first one is to establish a foundation of the Chern-MacPherson natural transformation for the category of quasi-projective Deligne-Mumford algebraic stacks (orbifolds) with proper representable morphisms. Furthermore, by the same mean, I gave an extension, for DM stacks mentioned above, of the Todd class transformation in the sense of Baum-Fulton-MacPherson and also the Hirzebruch class transformation in the sense of Brasselet-Schurmann-Yokura. The second one is that I tried to study the generating functions of singular Chern class of the Hilbert scheme of points on a smooth variety through the pushforward to the symmetric product. arguments. Finally, as a variant of enumerative geometry of singularities arising in differential topology, I studied about Vassiliev-type invariants and relative Thom polynomials for differentiable maps between smooth manifolds.
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Report
(4 results)
Research Products
(36 results)
