Local topology of reducible divisors

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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.
14 pages

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Algebraic Geometry, Algebraic Topology, 14F17, 14F45, 32S22, 32S55

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http://salesiana.dossiersoluciones.com/handle/123456789/66818

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0303215
 http://arxiv.org/abs/math/0303215

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arXiv