Studies on Characteristic Classes of Singular Varieties and Invariants of Singularities

奇异簇特征类与奇异性不变量的研究

基本信息

批准号：
10640084
负责人：
YOKURA Shoji
金额：
$ 2.11万
依托单位：
Kagoshima University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640084/
关键词：
singular variety characteristic class Milnor number Milnor class bivariant theory bivariant Chern class

项目摘要

(1). We showed that the proof of Parusinski-Pragacz's Theorem on the Parusinski's generalized Milnor number also works for the Milnor class.(2). By introducing a "q-deformed" local Euler obstruction, we constructed a "q-deformed" Chern-Schwartz-MacPhjerson class which generalize both the Chern-Mather class and the Chern-Schwartz-MacPherson class. (A purpose of this paper is to point out that the Chern-Mather class can be also captured as a natural transformation).(3). We obtained some results on bivariant constructible functions, such as the observation that the Chern-Schwartz-MacPherson class of a bivariant constructible function restricted to each fiber of a morphism is locally constant, etc.(4). Using the bivariant theoru of Fulton-MacPherson, we obtained some reasonable pull-back formulas for the Milnor class for certain morphisms.(5). By obtaining product formulas for the Milnor class, we obtained a Parusinski-Pragacz-type formula for the product of hypersuraces and also we could give some kind of geometric meaning to a certain cohomology class appearing in the Bruselet-Lehmann-Seade-Suwa's formula for the Milnor class, and also we obtained a Thom-Sebastiani-type formula for the Milnor class.(6). We showed that the existence of bivariant Chern class with values in the bivariant Chow groups is equivalent to the existence of the commutaive "Verdier-Riemann-Roch" diagram for the Chern-Schwartz-MacPherson class.

（1）。我们表明，帕鲁森斯基 - 普拉加斯（Parusinski-Pragacz）关于帕鲁森斯基（Parusinski）广义米尔诺（Milnor）编号的定理也适用于米尔诺（Milnor）类（2）。通过引入“ Q更符合”的本地Euler障碍，我们构建了一个“ Q更符合Q的” Chern-Schwartz-Macphjerson类，该类别概括了Chern-Mather阶级和Chern-Schwartz-Macpherson类。（本文的目的是指出，Chern-Mather类也可以作为自然转变捕获）（3）。我们在双变量构造函数上获得了一些结果，例如观察到的观察是，限制在每种形态的每种纤维的双变量构造函数的Chern-Schwartz-Macpherson类是局部恒定的，等等。（4）。使用Fulton-Macpherson的双变量定理，我们为Milnor类获得了一些合理的倾斜配方，以进行某些形态。（5）。 By obtaining product formulas for the Milnor class, we obtained a Parusinski-Pragacz-type formula for the product of hypersuraces and also we could give some kind of geometric meaning to a certain cohomology class appearing in the Bruselet-Lehmann-Seade-Suwa's formula for the Milnor class, and also we obtained a Thom-Sebastiani-type formula for the Milnor班级（6）。我们表明，在双变量的Chow组中存在具有值的双变量Chern类等同于Chern-Schwartz-Macpherson类的通勤“ Verdier-Riemann-Roch”图。