Symmetric Determinantal Singularities II: Equisingularity and SEIDS

TL;DR

This paper investigates the Whitney equisingularity of symmetric determinantal singularities, demonstrating how polar curve multiplicities in deformations can control equisingularity types.

Contribution

It introduces methods to analyze Whitney equisingularity in symmetric determinantal singularities using polar curve multiplicities in deformations.

Findings

Polar curve multiplicities determine Whitney equisingularity.

Deformation analysis links singularity types to geometric invariants.

Provides tools for classifying symmetric determinantal singularities.

Abstract

This paper is the second 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.