Characteristic varieties and Betti numbers of free abelian covers
type: Item
instance of: scholarly article
zbMATH Open document ID: 1352.57004
publication date: 2014-09-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/1111.5803
Mathematics Subject Classification ID: 57M10
Mathematics Subject Classification ID: 55N25
Mathematics Subject Classification ID: 14F35
Mathematics Subject Classification ID: 14H30
zbMATH DE Number: 6340344
zbMATH Keywords: free abelian covers
zbMATH Keywords: Betti numbers
zbMATH Keywords: characteristic varieties
zbMATH Keywords: Grassmannians
zbMATH Keywords: Schubert varieties
author: Alexander I. Suciu
MaRDI profile type: Publication
OpenAlex ID: W3101530662
arXiv ID: 1111.5803
DOI: 10.1093/IMRN/RNS246
published in: IMRN. International Mathematics Research Notices
title: Characteristic varieties and Betti numbers of free abelian covers
review text: The \({\mathbb{Z}}^r\)-covers of a finite CW-complex \(X\) are parametrized by the Grassmann variety of \(r\)-dimensional subspaces in the cohomology group \(H^1(X, {\mathbb{Q}})\). The subspaces corresponding to coverings having the first \(i\) Betti numbers finite form a subset \(\Omega_r^i(X)\) in this Grassmannian. The author studies these sets using the jumping loci for the homology of \(X\) with coefficients in rank one local systems. Special attention is given to the case when \(X\) is a smooth quasi-projective or projective variety.
reviewed by: Alexandru Dimca
description: scientific article; zbMATH DE number 6340344