论文标题
关于孤立奇异函数的变形
On deformations of isolated singularity functions
论文作者
论文摘要
我们研究了亚分析集或复杂的分析空间上分离的奇异性函数节点的多参数变形。我们证明，如果这种变形没有奇异点的合并，那么它具有恒定的拓扑类型。由于Lê\＆Ramanujam（1976）和Parusiński（1999）以及由于耶稣 - 阿尔梅达（Jesus-Almeida）和第一作者的最新结果，这扩展了一些古典结果。它还为$ \ c^3 $的一个复杂孤立奇异表面的单参数家族提供了足够的条件，以具有恒定的拓扑类型。另一方面，对于在孤立的决定性奇异性上定义的复杂孤立的奇异家庭，我们证明$μ$ - 概念意味着恒定的拓扑类型。
We study multi-parameters deformations of isolated singularity function-germs on either a subanalytic set or a complex analytic spaces. We prove that if such a deformation has no coalescing of singular points, then it has constant topological type. This extends some classical results due to Lê \& Ramanujam (1976) and Parusiński (1999), as well as a recent result due to Jesus-Almeida and the first author. It also provides a sufficient condition for a one-parameter family of complex isolated singularity surfaces in $\C^3$ to have constant topological type. On the other hand, for complex isolated singularity families defined on an isolated determinantal singularity, we prove that $μ$-constancy implies constant topological type.
