Characteristic classes of algebraic stacks and application to enumerative problems
| Project/Area Number |
24340007
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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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, 理学(系)研究科(研究院), 教授 (20264400)
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| Co-Investigator(Kenkyū-buntansha) |
NARUSE Hiroshi 山梨大学, 総合研究部, 教授 (20172596)
SUWA Tatsuo 北海道大学, 名誉教授 (40109418)
YOKURA Shoji 鹿児島大学, 学術研究院理工学域理学系, 教授 (60182680)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥16,250,000 (Direct Cost: ¥12,500,000、Indirect Cost: ¥3,750,000)
Fiscal Year 2015: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2014: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2013: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2012: ¥6,110,000 (Direct Cost: ¥4,700,000、Indirect Cost: ¥1,410,000)
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| Keywords | 特異点論 / 特性類理論 / チャーン類 / トム多項式 / 数え上げ幾何 / ホイットニー類 / 半代数的集合 / 特性類 / 国際研究者交流（フランス，ベトナム） / 写像の特異点論 / チャーン・シュワルツ・マクファーソン類 / 国際研究者交流（フランス，ドイツ，米国） / 国際情報交換（フランス，ブラジル） / 特異点 / Chern-Schwartz-MacPherson class / Hirzebruch class / Todd class / Thom polynomials / Hilbert scheme |
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| Outline of Final Research Achievements |
Seeking for the complete foundation of the enumerative theory of singularities of maps, I have developed singular Chern class theory on various moduli spaces; in particular, together with collaborators I completed a sequence of works on zeta functions of homology characteristic classes of Hilbert schemes of points on a non-singular variety; I applied the theory of equivariant singular Chern classes to the classification theory of map-germs, that made a new breakthrough for computing singular Milnor numbers.
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Report
(5 results)
Research Products
(36 results)
