$\mu$-constant deformations of functions on ICIS

TL;DR

This paper investigates conditions under which deformations of holomorphic functions on isolated complete intersection singularities (ICIS) maintain key invariants like Milnor number, Euler obstruction, and Bruce-Roberts number, enhancing understanding of singularity stability.

Contribution

It provides new criteria for $mbda$-constant deformations of functions on ICIS, linking invariants such as Milnor number, Euler obstruction, and Bruce-Roberts number.

Findings

Conditions for constant Milnor number established

Criteria for constant Euler obstruction derived

Results applicable to stability analysis of singularities

Abstract

We study deformations of holomorphic function germs $f:(X,0)\to\mathbb C$ where $(X,0)$ is an ICIS. We present conditions for these deformations to have constant Milnor number, Euler obstruction and Bruce-Roberts number.