Torsion points on the cohomology jump loci of compact K\"ahler manifolds

Botong Wang

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arXiv · 1312.6619

Torsion points on the cohomology jump loci of compact K\"ahler manifolds

Botong Wang

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Abstract

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.

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Botong Wang. 2013-12-23. Torsion points on the cohomology jump loci of compact K\"ahler manifolds. https://arxiv.org/abs/1312.6619

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