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Abstract:
The local systems on the complement of an arbitrary divisor
in a smooth complex projective variety contain a wealth of information
about the singularities of the divisor. We describe various
filtrations on local systems, their induced stratifications
on the space of unitary rank one local systems, and their
relation with the singularities of the divisor. Applications
include: some results about Hodge numbers of abelian covers, and some
results about singularity invariants (Hodge spectra, Bernstein-Sato
polynomials, and Denef-Loeser zeta functions) for hyperplane arrangements.
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