A generalization of the Milnor number
A generalization of the Milnor number
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Milnor 数的推广
DOI：
10.1007/bf01458431
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
A. Parusiński
中科院分区：
文献类型：
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作者：
A. Parusiński
Milnor在[7]中引入了复超曲面孤立奇点的Milnor数，并从多个方面对其进行了广泛的研究。这些研究都集中在奇点的局部性质上，本文的目的是将Milnor数的概念推广到非孤立奇点上。我们将给出一个定义，该定义适用于复流形中超曲面的奇点集的任何紧分支，并给出孤立奇点情况下的Milnor数。在第一节中，我们还研究了所定义数的一些简单性质，并给出了利用陈类和欧拉特征线的一个公式。
The Milnor number of an isolated singularity of a complex hypersurface was introduced by Milnor in [7] and afterwards widely investigated from many aspects. All these investigations have been concentrated on local properties of singularities.The aim of this paper is to extend the notion of Milnor number to nonisolated singularities. We shall give a definition which works for any compact component of the set of singular points of a hypersurface in a complex manifold and gives the Milnor number in the case of an isolated singularity. In Sect. 1 we also study some simple properties of the defined number and give a formula for it in terms of Chern classes and the Euler characteristic.