Cohomology jump loci of quasi-projective varieties

Abstract

We prove that the cohomology jump loci in the space of rank one local systems over a smooth quasi-projective variety are finite unions of torsion translates of subtori. The main ingredients are a recent result of Dimca-Papadima, some techniques introduced by Simpson, together with properties of the moduli space of logarithmic connections constructed by Nitsure and Simpson.

Final version, to appear in Ann. Sci. Ecole Norm. Sup

References in corpus (1)

• Kobayashi-Hitchin correspondence for tame harmonic bundles II

Cited by in corpus (2)

• Examples of topological spaces with arbitrary cohomology jump loci
• Cohomology jump loci of compact Kähler manifolds