Hodge modules on complex tori and generic vanishing for compact Kähler manifolds

Abstract

We extend the results of generic vanishing theory to polarizable real Hodge modules on compact complex tori, and from there to arbitrary compact Kähler manifolds. As applications, we obtain a bimeromorphic characterization of compact complex tori among compact Kähler manifolds, semi-positivity results, and a description of the Leray filtration for maps to tori.

34 pages. Final version, to appear in Geometry and Topology

References in corpus (1)

• Torsion points on the cohomology jump loci of compact Kähler manifolds

Cited by in corpus (4)

• Some results on the eventual paracanonical maps
• Standard canonical support loci
• Vanishing and injectivity for R-Hodge modules and R-divisors
• Irregular varieites with geometric genus one, theta divisors, and fake tori