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Non vanishing loci of Hodge numbers of local systems

A. Libgober
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Abstract

We show that closures of families of unitary local systems on quasiprojective varieties for which the dimension of a graded component of Hodge filtration has a constant value can be identified with a finite union of polytopes. We also present a local version of the theorem. This yields the "Hodge decomposition" of the set of unitary local systems with a non-vanishing cohomology extending Hodge decomposition of characteristic varieties of links of plane curves studied by the author earlier. We consider a twisted version of the characteristic varieties generalizing the twisted Alexander polynomials. Several explicit calculations for complements to arrangements are made.

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A. Libgober. 2008-10-17. Non vanishing loci of Hodge numbers of local systems. https://arxiv.org/abs/math/0701597

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