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arXiv · 2011.14184

Cohomology jump loci and absolute sets for singular varieties

Leonardo A. Lerer
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Abstract

We extend the notion of absolute subsets of Betti moduli spaces of smooth algebraic varieties to the case of normal varieties. As a consequence we prove that twisted cohomology jump loci in rank one over a normal variety are a finite union of translated subtori. We show that the same holds for jump loci twisted by a unitary local system in the case where the underlying variety $X$ is projective with $H^1(X,\mathbb{Q})$ pure of weight one. Lastly, we study the interaction of these loci with Hodge theoretic data naturally associated to the representation variety of fundamental groups of smooth projective varieties.

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Leonardo A. Lerer. 2020-11-28. Cohomology jump loci and absolute sets for singular varieties. https://arxiv.org/abs/2011.14184

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