Tame deformations of highly singular function germs

TL;DR

This paper establishes conditions under which deformations of real analytic functions with complex singularities maintain constant fibers, combining analytic and algebraic approaches to understand their stability.

Contribution

It introduces new criteria for fiber constancy in deformations of functions with non-isolated singularities, advancing the understanding of their stability.

Findings

Derived analytic conditions for fiber constancy.

Provided algebraic criteria for deformations.

Enhanced understanding of singularity stability in deformations.

Abstract

We give analytic and algebraic conditions under which a deformation of real analytic functions with non-isolated singular locus is a deformation with fibre constancy.