# Geometry of cohomology support loci for local systems I

@article{Arapura1996GeometryOC, title={Geometry of cohomology support loci for local systems I}, author={D. Arapura}, journal={arXiv: Algebraic Geometry}, year={1996} }

Let X be a Zariski open subset of a compact Kaehler manifold. In this paper, we study the set $\Sigma^k(X)$ of one dimensional local systems on X with nonvanishing kth cohomology. We show that under certain conditions (X compact, X has a smooth compactification with trivial first Betti number, or k=1) $\Sigma^k(X)$ is a union of translates of sets of the form $f^*H^1(T,C^*)$, where $f:X \to T$ is a holomorphic map to a complex Lie group which is an extension of a compact complex torus by a… Expand

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