The index of differential forms on complete intersections
type: Item
instance of: scholarly article
title: The index of differential forms on complete intersections
zbMATH Open document ID: 1336.14014
publication date: 2015-09-28T00:00:00Z
review text: The author computes the local topological index of a holomorphic 1-form on a quasi-homogeneous complete intersection isolated singularity in terms of the degrees of quasi-homogeneity type. Then the ungraded case is studied using the Lebelt and Cousin resolutions as well as Koszul complexes. This yields formulas for the local topological index in terms of ideals spanned by minors of maximal order in some matrices naturally associated to the geometric situation.
reviewed by: Alexandru Dimca
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 58A10
Mathematics Subject Classification ID: 14F40
Mathematics Subject Classification ID: 58A12
zbMATH DE Number: 6485781
zbMATH Keywords: local topological index
zbMATH Keywords: holomorphic 1-forms
zbMATH Keywords: complete intersections
author: Aleksandr G. Aleksandrov
MaRDI profile type: Publication
full work available at URL: s10688-015-0078-z
OpenAlex ID: W2003686303
cites work: The de Rham complex of a quasihomogeneous complete intersection
cites work: COHOMOLOGY OF A QUASIHOMOGENEOUS COMPLETE INTERSECTION
cites work: The index of vector fields and logarithmic differential forms
cites work: The topological index of vector fields at quasihomogeneous complete intersections
cites work: Q4183005
cites work: Q4274969
cites work: An algebraic formula for the index of a vector field on an isolated complete intersection singularity
cites work: THE GEOMETRY OF TORIC VARIETIES
cites work: Q4440922
cites work: HOMOLOGICAL INDEX FOR 1-FORMS AND A MILNOR NUMBER FOR ISOLATED SINGULARITIES
cites work: Q4267942
cites work: Der Gauß-Manin-Zusammenhang isolierter Singularitäten von vollständigen Durchschnitten
cites work: Invarianten quasihomogener vollständiger Durchschnitte
cites work: Q5513537
cites work: Reguläre Differentialformen
cites work: Local residues of holomorphic 1-forms on an isolated surface singularity
cites work: Torsion äußerer Potenzen von Moduln der homologischen Dimension 1
cites work: Freie Auflösungen äußerer Potenzen
cites work: On the index of a holomorphic vector field tangent to a singular variety
cites work: Q5343374
cites work: Some remarks on isolated singularity and their application to algebraic manifolds
cites work: Q3961117
cites work: Infinitesimal extensions of commutative algebras
DOI: 10.1007/S10688-015-0078-Z
published in: Functional Analysis and Its Applications
Recommended article: Q4860507
Recommended article: Q3188974
Recommended article: Q4966009
Recommended article: Differential forms on quasihomogeneous noncomplete intersections
Recommended article: The index of vector fields and logarithmic differential forms
Recommended article: Symmetric differential forms on complete intersection varieties and applications
Recommended article: Q4440922
Recommended article: Q3527643
Recommended article: Q3312954
Recommended article: Differential forms on singular varieties and cyclic homology
description: scientific article; zbMATH DE number 6485781