Equisingularity and EIDS

TL;DR

This paper explores Essentially Isolated Determinantal Singularities (EIDS), linking topological and geometric invariants to establish criteria for Whitney equisingularity in these complex singularities.

Contribution

It introduces a novel approach connecting topology and infinitesimal geometry to analyze EIDS and provides a criterion for their Whitney equisingularity.

Findings

Established a connection between topological and geometric invariants of EIDS.

Provided a criterion for Whitney equisingularity of EIDS families.

Enhanced understanding of the landscape perspective in singularity theory.

Abstract

The study of Essentially Isolated Determinantal Singularites or EIDS was initiated by Ebeling and Gusein-Zade. They are non-smoothable as determinantal singularities, and in general have non-isolated singularities. Their singularities are generic in a deleted neighborhood of the origin, hence their description as "essentially isolated". In this paper we study these singularities from the "landscape" point of view introduced in MathArxiv 1501.00201. Using this point of view we show a connection between invariants coming from the topology of the stabilization and invariants coming from the infinitesimal geometry of the singularity. This gives us a criterion for the Whitney equisingularity of EIDS families.