Hodge spectrum of hyperplane arrangements

Details Hodge spectrum of hyperplane arrangements Hodge spectrum of hyperplane arrangements

2008-09-19

arxiv.org/abs/0809.3443v2

Mathematics

Algebraic Geometry

v2: added references to Prof. Libgober's work

Scientific paper

In this article there are two main results. The first result gives a formula, in terms of a log resolution, for the graded pieces of the Hodge filtration on the cohomology of a unitary local system of rank one on the complement of an arbitrary divisor in a smooth projective complex variety. The second result is an application of the first. We give a combinatorial formula for the spectrum of a hyperplane arrangement. M. Saito recently proved that the spectrum of a hyperplane arrangement depends only on combinatorics. However, a combinatorial formula was missing. The formula is achieved by a different method.

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