On deformations of isolated singularity functions
Complex Variables
2022-06-22 v1 Algebraic Geometry
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 to have constant topological type. On the other hand, for complex isolated singularity families defined on an isolated determinantal singularity, we prove that -constancy implies constant topological type.
Cite
@article{arxiv.2206.10035,
title = {On deformations of isolated singularity functions},
author = {Aurélio Menegon and Miriam da Silva Pereira},
journal= {arXiv preprint arXiv:2206.10035},
year = {2022}
}