On deformation with constant Milnor number and Newton polyhedron

TL;DR

This paper proves that under certain conditions, families of isolated hypersurface singularities with constant Milnor number are topologically trivial and equimultiple, extending understanding of singularity deformation.

Contribution

It establishes topological triviality and equimultiplicity for μ-constant hypersurface singularity families satisfying Kouchnirenko's nondegeneracy.

Findings

μ-constant families are topologically trivial

Such families are also equimultiple

Results apply under Kouchnirenko's nondegeneracy condition

Abstract

We show that every $\mu$-constant family of isolated hypersurface singularities satisfying a nondegeneracy condition in the sense of Kouchnirenko, is topologically trivial, also is equimultiple.