Poincaré-Hopf Theorem for Isolated Determinantal Singularities

N. G. Grulha; M. S. Pereira; H. Santana

paper

Poincaré-Hopf Theorem for Isolated Determinantal Singularities

arXiv:2605.06041

Abstract

Let $X$ be a projective algebraic $d$ -variety endowed with isolated determinantal singularities, and let $ω$ be a $1$ -form on $X$ exhibiting a finite number of singularities (in the stratified sense). Under some technical conditions, we use two generalizations of Poincaré-Hopf index with the goal of proving a Poincaré-Hopf Type Theorem for $X$ .