Research on Complex Analytic Geometry and Singularity Theory

复解析几何与奇异性理论研究

基本信息

批准号：
07454011
负责人：
SUWA Tatsuo
金额：
$ 4.99万
依托单位：
Hokkaido University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

项目摘要

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.

这项研究主要是关于矢量场和全态奇异叶子的指标和残基进行的，奇异品种的特征类别，Cech-DE Rham的同时协同理论和对分层空间的整合理论。让我们更具体。（1）与J.Seade在残留定理上为开放式流形及其应用中的叶子残留物的残留定理进行合作。有关此的联合论文已发表在Mathematische Annalen。（2）在与J.Seade的另一项合作中，我们研究了具有孤立奇异性品种的矢量领域的各种指数，我们获得了此类品种的“相邻公式”。结果写在联合纸中。（3）作为（2）中公式的应用，获得了与局部完整交点的化学公式，并获得了与孤立的奇异性。该结果已在巴黎的C.R.Acad.Sci。（4）作为（2）中公式的概括（4）与D.Lehmann和J.Seade合作，我们引入了广义Milnor数字，并获得了类似的品种的公式，并具有可能非相差的奇异性。结果写在联合纸中。（5）在与b.khanedani的联合作品中，我们研究了复杂表面上奇异的全态叶子的不变性，并获得了各种公式。有关这些的联合论文将出现在北海道数学（6）中，在与T.Honda的联合作品中，我们证明了在复杂表面上的Meromorthic功能的残留公式，并提供了一些应用。结果是用联合论文写的。（7）在与J.-P.Brasselet的合作中，我们研究了与Sinular Holomormorphic Foliation相关的NASH修饰，并且在某些情况下，我们证明了Baum-Bott的猜想。结果写在联合论文中。