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Oberseminar WiSe 2010/11 Zusammenfassung des Vortrags von Nero Budur (Notre Dame, USA)

Local systems and singularities

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.