Desingularization of generic symmetric and generic skew-symmetric determinantal singularities

TL;DR

This paper presents a method for resolving singularities in generic symmetric and skew-symmetric determinantal varieties using symmetry-preserving matrix operations and inductive reasoning.

Contribution

It introduces a novel approach that maintains symmetry during desingularization, advancing the understanding of determinantal singularities.

Findings

Successful resolution of symmetric determinantal singularities

Effective desingularization of skew-symmetric determinantal singularities

Development of symmetry-preserving matrix operations

Abstract

We discuss how to resolve generic skew-symmetric and generic symmetric determinantal singularities. The key ingredients are (skew-) symmetry preserving matrix operations in order to deduce an inductive argument.