On indices of 1-forms on determinantal singularities

2008/06/02 by Wolfgang Ebeling, Ebeling, W., S. M. Gusein‐Zade +1 · 2 citations
Chemistry · Mathematics · #14B05 #14M12 #58A10 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Molecular spectroscopy and chirality

paper · pdf · doi:10.48550/arxiv.0806.0219

openalex publication_date 2008/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider 1-forms on, so called, essentially isolated determinantal singularities (a natural generalization of isolated ones), show how to define analogues of the Poincaré--Hopf index for them, and describe relations between these indices and the radial index. For isolated determinantal singularities, we discuss properties of the homological index of a holomorphic 1-form and its relation with the Poincaré--Hopf index.

Citations

• Cohen-Macaulay Rings, Invariant Theory, and the Generic Perfection of Determinantal Loci

Cited by

• Classification of normal toric surfaces resolved by a single Nash blowup
• Non-normalized Nash blowup fails to resolve singularities in dimension three

Related

• Homological index for 1-forms and a Milnor number for isolated singularities
• Poincaré-Hopf Theorem for Isolated Determinantal Singularities
• Proportionality of Indices of 1-Forms on Singular Varieties
• Indices of 1-forms on an isolated complete intersection singularity
• Indices of vector fields and 1-forms on singular varieties