2011 Fiscal Year Final Research Report
Localization theory of Atiyah classes and its applications
| Project/Area Number |
21540060
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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 |
SUWA Tatsuo 北海道大学, 名誉教授 (40109418)
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| Co-Investigator(Renkei-kenkyūsha) |
OHMOTO Toru 北海道大学, 理学研究院, 准教授 (20264400)
OKA Mutsuo 東京理科大学, 理学部, 教授 (40011697)
KAWAZUMI Nariya 東京大学, 数理科学研究科, 准教授 (30214646)
TAKEUCHI Kiyoshi 筑波大学, 物質科学研究科, 准教授 (70281160)
TAJIMA Shinichi 筑波大学, 物質科学研究科, 教授 (70155076)
NAKAMURA Yayoi 近畿大学, 理工学部, 講師 (60388494)
YOKURA Shoji 鹿児島大学, 理学部, 教授 (60182680)
YOSHIKAWA Kenichi 京都大学, 理学研究科, 教授 (20242810)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 複素解析幾何 / 特性類の局所化 / 留数 / チャーン類 / アティア類 / 特異多様体 / 特異正則分布 |
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| Research Abstract |
(1) Concerning the localization theory of Atiyah classes, with collaboration of M. Abate, F. Bracci and F. Tovena, we established the following fundamental theories : (1) a simple definition of Atiyah classes suitable for the localization theory,(2) Cech-Dolbeault cohomology theory,(3) introduction of the complex analytic Thom class,(4) proof of a Bott type vanishing theorem in terms of Atiyah forms.
(2) Concerning the degeneracy loci problem of a homomorphism of vector bundles, with collaboration of T. Ohmoto, we started to try to prove the Thom-Porteous formula localized at the degeneracy loci. This is done by constructing a universal localization of a Schur polynomial of Chern. It is a vast generalization of the Thom class of a vector bundle.
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