Grant-in-Aid for Scientific Research (B)
|Research Institution||Hokkaido University|
SUWA Tatsuo Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (40109418)
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)
泉屋 周一 北海道大学, 大学院・理学研究科, 教授 (80127422)
山口 佳三 北海道大学, 大学院・理学研究科, 教授 (00113639)
中村 郁 北海道大学, 大学院・理学研究科, 教授 (50022687)
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)
|Project Fiscal Year
1995 – 1996
Completed(Fiscal Year 1996)
|Budget Amount *help
¥7,800,000 (Direct Cost : ¥7,800,000)
Fiscal Year 1996 : ¥3,700,000 (Direct Cost : ¥3,700,000)
Fiscal Year 1995 : ¥4,100,000 (Direct Cost : ¥4,100,000)
|Keywords||vector fields / singular foliations / indices and residues / localization / characteristic classes / singular varieties / ベクトル場 / 特異葉層構造 / 指数と留数 / 局所化 / 特性類 / 特異多様体 / ベットル場 / 正則ベクトル場 / 留数|
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.