Non vanishing loci of Hodge numbers of local systems |
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Authors: | Anatoly Libgober |
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Affiliation: | (1) Department of Mathematics, University of Illinois, Chicago, IL 60607, USA |
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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. A. Libgober was supported by National Science Foundation grant. |
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Keywords: | KeywordHeading" >Mathematics Subject Classification (2000) 32J25 (14C30, 14F35, 14F40, 14F45, 32C17, 57M10, 57M12, 57M25) |
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