Non-degenerate jump of Milnor numbers of surface singularities

TL;DR

This paper provides a formula for the minimal change in Milnor numbers during non-degenerate deformations of certain surface singularities, advancing understanding of their stability and behavior.

Contribution

It introduces a specific formula for the jump in Milnor numbers for a class of surface singularities under non-degenerate deformations.

Findings

Derived a formula for the Milnor number jump in surface singularities

Applicable to non-degenerate deformations of specific singularity classes

Enhances understanding of singularity stability and deformation behavior

Abstract

The jump of the Milnor number of an isolated singularity $f_0$ is the minimal non-zero difference between the Milnor numbers of $f_0$ and one of its deformations $(f_s)$. We give a formula for the jump in some class of surface singularities in the case deformations are non-degenerate.