We show in this paper that the set of irreducible components of the family of Galois coverings of with Galois group isomorphic to is in bijection with the set of possible numerical types. In this special case the numerical type is the equivalence class (for automorphisms of ) of the function which to each conjugacy class in associates the number of branch points whose local monodromy lies in the class .
Cite this article
Fabrizio Catanese, Michael Lönne, Fabio Perroni, Irreducibility of the space of dihedral covers of the projective line of a given numerical type. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 22 (2011), no. 3, pp. 291–309DOI 10.4171/RLM/601