Title: ORBIFOLD GROUPS, QUASI-PROJECTIVITY AND COVERS
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 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.Read More