%0 Journal Article
%T Torsion points on the cohomology jump loci of compact K£¿hler manifolds
%A Botong Wang
%J Mathematics
%D 2013
%I arXiv
%X We prove that each irreducible component of the cohomology jump loci of rank one local systems over a compact K\"ahler manifold contains at least one torsion point. This generalizes a theorem of Simpson for smooth complex projective varieties. An immediate consequence is the conjecture of Beauville and Catanese for compact K\"ahler manifolds. We also provide an example of a compact K\"ahler manifold, whose cohomology jump loci can not be realized by any smooth complex projective variety.
%U http://arxiv.org/abs/1312.6619v2