Non vanishing loci of Hodge numbers of local systems

Details Non vanishing loci of Hodge numbers of local systems Non vanishing loci of Hodge numbers of local systems

2007-01-21

arxiv.org/abs/math/0701597v4

Mathematics

Algebraic Geometry

Final version. To appear in Manuscripta Mathematica

Scientific paper

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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