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

Abstract

In this work, we investigate the connections between the local Euler obstruction and the Poincaré-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.