Characteristic varieties and Betti numbers of free abelian covers
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.
scientific article; zbMATH DE number 6340344