Equisingularity of families of isolated determinantal singularities

TL;DR

This paper investigates the topological triviality and Whitney equisingularity of families of isolated determinantal singularities, extending classical results to this broader class using invariants like the vanishing Euler characteristic and polar multiplicities.

Contribution

It establishes a Le-Ramanujam type theorem and extends Whitney equisingularity criteria to isolated determinantal singularities, broadening the understanding of their topological and geometric properties.

Findings

Provides a criterion for topological triviality using the vanishing Euler characteristic.

Extends Whitney equisingularity conditions via constancy of polar multiplicities.

Generalizes classical results to a new class of singularities.

Abstract

We study the topological triviality and the Whitney equisingularity of a family of isolated determinantal singularities. On one hand, we give a L\^e-Ramanujam type theorem for this kind of singularities by using the vanishing Euler characteristic. On the other hand, we extend the results of Teissier and Gaffney about the Whitney equisingularity of hypersurfaces and complete intersections, respectively, in terms of the constancy of the polar multiplicities.