Local topology of reducible divisors

Details Local topology of reducible divisors Local topology of reducible divisors

2003-03-18

arxiv.org/abs/math/0303215v2

Mathematics

Algebraic Geometry

14 pages

Scientific paper

We show that the universal abelian cover of the complement to a germ of a reducible divisor on a complex space $Y$ with isolated singularity is $(dimY-2)$-connected provided that the divisor has normal crossings outside of the singularity of $Y$. We apply this result to obtain a vanishing property for the cohomology of local systems of rank one and we also study vanishing in the case of local systems of higher rank. This second version contains a corrected proof of Corollary 4.1 from the first version.

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