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摘要翻译：
研究了超曲面奇点的Milnor纤维的Euler特性。这个不变量是根据位于原始奇异点和它的Milnor纤维之间的纤维的欧拉特性和与位于中间的纤维的地层有关的欧拉特性给出的。由此我们可以导出Massey和Siersma关于具有一维临界轨迹的奇点的一个结果。该结果也应用于均匀性的研究。著名的Brian\c{c}on-Speder-Teissier结果表明，一族孤立超曲面奇点是等量的当且仅当其$\mu^*$-序列是常数。我们证明了如果从n-空间到(n+1)-空间的Corank1复解析映象族的相似序列是常数，则该映象族的映象是等量的。对于从3-空间到4-空间的Corank1映射族，我们证明了相反的情形也是成立的。
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英文标题：
《Equisingularity and The Euler Characteristic of a Milnor Fibre》
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作者：
Kevin Houston
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Complex Variables 复变数
分类描述：Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数，自守群作用与形式，伪凸性，复几何，解析空间，解析束
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英文摘要：
We study the Euler characteristic of the Milnor fibre of a hypersurface singularity. This invariant is given in terms of the Euler characteristic of a fibre in between the original singularity and its Milnor fibre and in terms of the Euler characteristics associated to strata of the in-between fibre. From this we can deduce a result of Massey and Siersma regarding singularities with a one-dimensional critical locus. The result is also applied to the study of equisingularity. The famous Brian\c{c}on-Speder-Teissier result states that a family of isolated hypersurface singularities is equisingular if and only if its $\mu ^*$-sequence is constant. We show that if a similar sequence for a family of corank 1 complex analytic mappings from n-space to (n+1)-space is constant, then the image of the family of mappings is equisingular. For families of corank 1 maps from 3-space to 4-space we show that the converse is true also.
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PDF链接：
https://arxiv.org/pdf/0807.0574
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