  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.

Algebraic Geometry;Algebraic Topology