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Non vanishing loci of Hodge numbers of local systems

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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 this 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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Authors and Affiliations

  1. Department of Mathematics, University of Illinois, Chicago, IL, 60607, USA

    Anatoly Libgober

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  1. Anatoly Libgober
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Correspondence to Anatoly Libgober.

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A. Libgober was supported by National Science Foundation grant.

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Libgober, A. Non vanishing loci of Hodge numbers of local systems. manuscripta math. 128, 1–31 (2009). https://doi.org/10.1007/s00229-008-0221-8

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  • DOI: https://doi.org/10.1007/s00229-008-0221-8

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