Poincar\'e-Hopf Theorem for Isolated Determinantal Singularities

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

Poincar\'e-Hopf Theorem for Isolated Determinantal Singularities

Geometric Topology 2026-04-17 v4

Authors: N. G. Grulha , M. S. Pereira , H. Santana

Abstract

Let $X \subset\mathbb{P}^r$ be a projective $d$ -variety with isolated determinantal singularities and $\omega$ 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 Poincar\'e-Hopf index with the goal of proving a Poincar\'e-Hopf Type Theorem for $X$ .

Keywords

projective varieties singularity theory toric varieties

Cite

@article{arxiv.2007.05026,
  title  = {Poincar\'e-Hopf Theorem for Isolated Determinantal Singularities},
  author = {N. G. Grulha and M. S. Pereira and H. Santana},
  journal= {arXiv preprint arXiv:2007.05026},
  year   = {2026}
}

Comments

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

Poincar\'e-Hopf Theorem for Isolated Determinantal Singularities

Abstract

Keywords

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