Irreducibility of the space of dihedral covers of the projective line of   a given numerical type
  We show in this paper that the set of irreducible components of the family of Galois coverings of P^1_C with Galois group isomorphic to D_n is in bijection with the set of possible numerical types. In this special case the numerical type is the equivalence class (for automorphisms of D_n) of the function which to each conjugacy class \mathcal{C} in D_n associates the number of branch points whose local monodromy lies in the class \mathcal{C}. 
Fabrizio Catanese, Michael L\"onne, Fabio Perroni
math.AG math.GT