The Euler obstruction of a $1$-form on a determinantal singularity

TL;DR

This paper explores the relationship between the Euler obstruction and the Poincaré-Hopf-Nash index of 1-forms on determinantal singularities, providing explicit computations for functions with isolated stratified singularities.

Contribution

It establishes connections between topological invariants and indices in determinantal singularities and offers explicit calculations for specific cases.

Findings

Established links between Euler obstruction and PHN index in determinantal singularities.

Provided explicit formulas for Euler obstruction of functions with isolated stratified singularities.

Enhanced understanding of singularity invariants in algebraic geometry.

Abstract

In this work, we investigate the connections between the local Euler obstruction and the Poincar\'e-Hopf-Nash (PHN) index of a $1$-form in the setting of determinantal singularities. As an application, we provide explicit computations of the Euler obstruction of a function with a stratified isolated singularity at the origin defined on an IDS with rigid singularities.