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Abstract: The abelian branched covers of the complex projective plane can be used to get information about the topology, and in particular about the fundamental group, of the complement to the branching set. We show how the growth of the Betti numbers in towers of abelian covers is related to the global geometry of the set of singularities of the branching curve and how it allows to detect holomorphic maps of the complements onto curves. This leads to applications to fundamental groups of complements to arrangements of hyperplanes.
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alexsuciu@neu.edu