Poincaré-Hopf Theorem for Isolated Determinantal Singularities

2020/07/09 by Nivaldo G. Grulha, Grulha, N. G., M. S. Pereira +3
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.2007.05026

openalex publication_date 2020/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X ⊂ℙ^r be a projective d-variety with isolated determinantal singularities and ω 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.

Related

• On indices of 1-forms on determinantal singularities
• Codimension Two Determinantal Varieties with Isolated Singularities
• Proportionality of Indices of 1-Forms on Singular Varieties
• Regularity of structure sheaves of varieties with isolated singularities
• Invariants of D(q,p) singularities