Poincaré-Hopf Theorem for Isolated Determinantal Singularities

Abstract

Let $X\subset {\mathbb{P}}^r$ be a projective $d$-variety with isolated determinantal singularities and $\ddot{I}‰$ be a $1$-form on $X$ with a finite number of singularities (in the stratified sense). Under some technical conditions on $r$ we use two generalization of Poincaré-Hopf index with the goal of proving a Poincaré-Hopf Type Theorem for $X$.

There is a mistake in Section 2 that must be corrected in order to rewrite the presented results