Poincar\'e-Hopf Theorem for Isolated Determinantal Singularities

Let $X$ be a projective algebraic $d$-variety endowed with isolated determinantal singularities, and let $\omega$ 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 Poincar\'e-Hopf index with the goal of proving a Poincar\'e-Hopf Type Theorem for $X$.