Cohomology jump loci of quasi-compact Kähler manifolds

Abstract

We give two applications of the exponential Ax-Lindemann Theorem to local systems. One application is to show that for a connected topological space, the existence of a finite model of the real homotopy type implies linearity of the cohomology jump loci around the trivial local system. Another application is the linearity of the cohomology jump loci of rank one local systems on quasi-compact Kähler manifolds.

References in corpus (2)

• A non-archimedean Ax-Lindemann theorem
• Recent results on cohomology jump loci

Cited by in corpus (2)

• Absolute sets and the Decomposition Theorem
• Mixed Hodge structures on cohomology jump ideals