Irreducibility of the space of dihedral covers of the projective line of a given numerical type

Details Irreducibility of the space of dihedral covers of the projective line of a given numerical type Irreducibility of the space of dihedral covers of the projective line of a given numerical type

2011-02-02

arxiv.org/abs/1102.0490v1

Mathematics

Algebraic Geometry

18 pages, to appear in Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., volume in memory of Giov

Scientific paper

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}.

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