Symmetric Determinantal Singularities I: The Multiplicity of the Polar Curve

TL;DR

This paper explores how the multiplicity of polar curves in symmetric determinantal singularities can be used to understand Whitney equisingularity, providing new insights into the deformation behavior of these singularities.

Contribution

It introduces a novel approach linking polar curve multiplicities to Whitney equisingularity in symmetric determinantal singularities.

Findings

Multiplicity of polar curves controls Whitney equisingularity.

Provides a framework for analyzing deformations of symmetric determinantal singularities.

Abstract

This paper is the first part of a two part paper which introduces the study of the Whitney Equisingularity of families of Symmetric determinantal singularities. This study reveals how to use the multiplicity of polar curves associated to a generic deformation of a singularity to control the Whitney equisingularity type of these curves.