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Local topology of reducible divisors

Alexandru Dimca·Anatoly Libgober
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Abstract

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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Alexandru Dimca, Anatoly Libgober. 2003-11-12. Local topology of reducible divisors. https://arxiv.org/abs/math/0303215

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