Calculation of Milnor number of isolated singularity of complete intersection
Calculation of Milnor number of isolated singularity of complete intersection
复制标题
完全交集孤立奇异点的微数计算
DOI：
10.1007/bf01078597
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发表时间：
1974
影响因子：
0.4
通讯作者：
D. Tráng
中科院分区：
文献类型：
--
作者：
D. Tráng
本文给出了完全相交孤立奇点的Milnor数的一个公式。计算方法类似于[7]和[8]中用于超曲面的方法。对于完全相交的情况下，这种方法是建议作者在1969年由GN Tyurina。1.1.最近Gruel [1，2]对完全相交的孤立奇点的Milnor数提出了一个类似的公式。Greuel的证明是代数的，而我们的证明是拓扑的，并且它使得有可能同时获得哈姆的以下结果：如果由方程j I= 0. fk= 0在点0 EC n处具有孤立奇点，则对于几乎所有足够小的（et..... e~）~ C k解析集的交]，= s，....，]若k= e~具有一个半径足够小且以原点为中心的球面B~ Cn，则它将是一个非奇异解析流形，其同伦类型为真实的维数为nk的球面的并g（X，0），其中它（X，0）定义为X在0处的Milnor数.
In this paper we give a formula for the Milnor number of an isolated singularity of complete intersection. The method of calculation is similar to the method used in [7] and [8] for hypersurfaces. For the case of complete intersection this method was suggested to the author in 1969 by GN Tyurina.1.1. Let us note that recently Gruel [1, 2] has proposed a similar formula for the Milnor number of an isolated singularity of complete intersection. Greuel's proof is algebraic, whereas our proof is topological and it makes it possible to obtain at the same time also the following result of Hamm: if an analytic complete intersection X specified by the equations j I= 0...., fk= 0 has at the point 0 EC n an isolated singularity, then for almost all sufficiently small (et..... e~)~ C k the intersection of an analytic set],= s,....,] k= e~ witha sphere B~ C n of sufficiently small radius and centered at the origin will be a nonsingular analytic manifold that has the homotopy type of a union g (X, 0) of spheres of real dimension nk, where it (X, 0) is by definition the Milnor number of X at 0.