1996 Fiscal Year Final Research Report Summary
Research on Complex Analytic Geometry and Singularity Theory
| Project/Area Number |
07454011
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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) |
OKA Mutsuo Tokyo Metropolitan Univ., Fac.of Sci., Prof., 理学部, 教授 (40011697)
HONDA Naofumi Hokkaido Univ., Grad.School of Sci., Lecturer, 大学院・理学研究科, 講師 (00238817)
KAWAZUMI Nariya Hokkaido Univ., Grad.School of Sci., Assoc.Prof., 大学院・理学研究科, 助教授 (30214646)
NAKAI Isao Hokkaido Univ., Grad.School of Sci., Assoc.Prof., 大学院・理学研究科, 助教授 (90207704)
ISHIKAWA Goo Hokkaido Univ., Grad.School of Sci., Assoc.Prof., 大学院・理学研究科, 助教授 (50176161)
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| Project Period (FY) |
1995 – 1996
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| Keywords | vector fields / singular foliations / indices and residues / localization / characteristic classes / singular varieties |
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| Research Abstract |
The research was done mainly on the indices and residues of vector fields and holomorphic singular foliations, the charactreistic classes of singular varieties, the Cech-de Rham cohomology theory and integration theory on stratified spaces. Let us be more specific.
(1) Collaboration with J.Seade on the residue theorem for the Baum-Bott residues of foliations on open manifolds and its applications. The joint paper on this has been published in Mathematische Annalen.
(2) In another collaboration with J.Seade, we investigated various indices of vector fields on varieties with isolated singularities and we obtained an "adjunction formula" for such varieties. The results are written in a joint paper.
(3) As an application of the formula in (2), a formula for the Chem-Schwartz-MacPherson class of a local complete intersection variety with isolated singularities is obtained. The result has been published in C.R.Acad.Sci., Paris.
(4) As a generalization of the formula in (2), in a collaboration with D.Lehmann and J.Seade, we introduced a generalized Milnor number and obtained a similar formula for varieties with possibly non-isolated singularities. The results are written in a joint paper.
(5) In a joint work with B.Khanedani, we studied the invariants of singular holomorphic foliations on complex surfaces and obtained various formulas. The joint paper on these will appear in Hokkaido Math.J.
(6) In a joint work with T.Honda, we proved a residue formula for meromorphic functions on complex surfaces and gave some applications. The results are written in a joint paper.
(7) In a collaboration with J.-P.Brasselet, we studied the Nash modification associated with a sinular holomorphic foliation and, as an application, we proved a conjecture of Baum-Bott in some cases. The results are written in a joint paper.
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