Invariants of Non-Isolated Singularities of Hypersurfaces

TL;DR

This paper extends existing results on hypersurface singularities with smooth singular loci, exploring their invariants and applications to Yomdin-type isolated singularities through the study of transversal discriminants.

Contribution

It generalizes previous work on morsifications of hypersurfaces with smooth singular loci and investigates the relationship between transversal discriminants and algebraic invariants.

Findings

Generalized results on morsifications of hypersurfaces with smooth singular locus

Analyzed the transversal discriminant and its relation to algebraic invariants

Applied findings to Yomdin-type isolated singularities

Abstract

In this paper we generalize some results by Siersma, Pellikaan, and de Jong regarding morsifications of singular hypersurfaces whose singular locus is a smooth curve, and present some applications to the study of Yomdin-type isolated singularities. In order to prove these results, we discuss the transversal discriminant of such singularities and how it relates to other algebraic and topological invariants.