Bekka's $(c)$-regularity condition and families of line singularities with constant L\^e numbers

TL;DR

This paper demonstrates that specific deformation families of line singularities with constant L extsuperscript{e} numbers satisfy Bekka's (c)-regularity, leading to topological equisingularity, extending previous results for isolated singularities.

Contribution

It establishes Bekka's (c)-regularity for families of line singularities with constant L extsuperscript{e} numbers, proving topological equisingularity in this context.

Findings

Families satisfy Bekka's (c)-regularity condition

Families are topologically equisingular

Results extend to line singularities from isolated cases

Abstract

We show that the natural stratifications arising from certain deformation families of line singularities with constant L\^e numbers satisfy Bekka's $(c)$-regularity condition. As a corollary, we obtain that these families are topologically equisingular. Similar results for families of isolated singularities were established by Abderrahmane.