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arXiv · 2206.10035

On deformations of isolated singularity functions

Aurélio Menegon·Miriam da Silva Pereira
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Abstract

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 L\^e \& Ramanujam (1976) and Parusi\'nski (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 $\mu$-constancy implies constant topological type.

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Aurélio Menegon, Miriam da Silva Pereira. 2022-06-20. On deformations of isolated singularity functions. https://arxiv.org/abs/2206.10035

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