Orbifold groups, quasi-projectivity and covers

Journal of Singularities
volume 5 (2012), 33-47
Proceedings of the International Conference on Singularity Theory and Applications, Hefei, China, July 25-31, 2011

Received 1 March 2012. Received in revised form 26 April 2012.

DOI: 10.5427/jsing.2012.5c

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Abstract:

We discuss properties of complex algebraic orbifold groups, their characteristic varieties, and their abelian covers. In particular, we deal with the question of (quasi)-projectivity of orbifold groups. We also prove a structure theorem for the variety of characters of normal-crossing quasi-projective orbifold groups. Finally, we extend Sakuma's formula for the first Betti number of abelian covers of orbifold fundamental groups. Several examples are presented, including a compact orbifold group which is not projective and a Zariski pair of plane curves in P^2 that can be told by considering an unbranched cover of P^2 with an orbifold structure.

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