The {\L}ojasiewicz exponent in non-degenerate deformations of surface singularities

TL;DR

This paper proves that the { extL}ojasiewicz exponent remains constant during non-degenerate $mbda$-constant deformations of surface singularities, confirming a question posed by Teissier and advancing understanding of singularity invariants.

Contribution

It establishes the invariance of the { extL}ojasiewicz exponent in a specific class of surface singularity deformations, addressing a longstanding open question.

Findings

{ extL}ojasiewicz exponent is constant in non-degenerate $mbda$-constant deformations

Confirms a conjecture by B. Teissier regarding singularity invariants

Advances the understanding of deformation invariants in algebraic geometry

Abstract

We prove the constancy of the {\L}ojasiewicz exponent in non-degenerate $\mu$-constant deformations of surface singularities. This is a positive answer to a question posed by B. Teissier.