2001 Fiscal Year Final Research Report Summary
Research on Characteristic Classes of Singular Varieties
| Project/Area Number |
11440014
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 Hokkaido Univ. Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (40109418)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIKAWA Goo Hokkaido Univ. Grad. School of Sci., Asso. Prof., 大学院・理学研究科, 助教授 (50176161)
IZUMIYA Shuichi Hokkaido Univ. Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (80127422)
NAKAMURA Iku Hokkaido Univ. Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (50022687)
OKA Mutsuo Tokyo Metropolitan Univ. Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (40011697)
SHIMADA Ichiro Hokkaido Univ. Grad. School of Sci., Asso. Prof., 大学院・理学研究科, 助教授 (10235616)
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| Project Period (FY) |
1999 – 2001
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| Keywords | singular varieties / localization of characteristic classes / Schwartz-MacPherson class / Fulton-Johnson class / Milnor class / multiplicity / coherent sheaves / Riemann-Roch theorem |
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| Research Abstract |
Directed by the head investigator Suwa, the research on characteristic of singular varieties, in particular the theory of Milnor classes and related topics have been performed, as described in the research proposal, We obtained an explicit formula for the Minor class of a non- singular component of singular variety, the notion of the homology Chern class is introduced. The Riemann-Roch theorem for embeddings of singular varieties are proved arid used to compute the Chern class of the tangent sheaf of a singular variety. As an application of the theory of localization of characteristic classes, we defined, for functions on singular varieties the notion of multiplicity at the singularity, gave the method to compute them and proved, in the global situation, the "multiplicity formula", which generalized well-known classical formula in the non-singular case. We also gave a direct and geometric proof of the Lefschetz fixed point formula for the de Rham and Dolbeault complexes.
The other investigators collaborated in the above projects and also obtained many other results in the subjects such as : the moduli space of Abelian varieties, me McKay correspondence of simple singularities, developable surfaces of curves in the Euclidean space and classification of singularities of Dalboux sphere representations, stability of singular Lagrangian varieties, singular fibers of elliptic K3 surges and the torsion subgroup of the Mordell-Weli group, geometry of sextic curves of torus type and the geometry of dual curves, an alternative proof of the algebraic independence of the Monta-Mumfoixl classes, parital answer to the Akita conjecture on the mapping class group.
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