On indices of 1-forms on determinantal singularities
W. Ebeling, S. M. Gusein-Zade

TL;DR
This paper extends the concept of indices for 1-forms to essentially isolated determinantal singularities, exploring their properties and relations to classical indices like the Poincaré-Hopf and radial indices.
Contribution
It introduces analogues of the Poincaré-Hopf index for 1-forms on determinantal singularities and examines their properties and interrelations.
Findings
Defined indices for 1-forms on determinantal singularities
Established relations between these indices and the radial index
Analyzed properties of the homological index for isolated cases
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 Poincar\'e--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 Poincar\'e--Hopf index.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Molecular spectroscopy and chirality · Algebraic structures and combinatorial models
