Orbifold groups, quasi-projectivity and covers

Details Orbifold groups, quasi-projectivity and covers Orbifold groups, quasi-projectivity and covers

2012-03-07

arxiv.org/abs/1203.1645v1

Mathematics

Algebraic Geometry

20 pages

Scientific paper

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 projective curves that can be told by considering an unbranched cover of the projective plane with an orbifold structure.

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