The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Rendiconti Lincei - Matematica e Applicazioni


Full-Text PDF (155 KB) | Metadata | Table of Contents | RLM summary
Volume 22, Issue 3, 2011, pp. 291–309
DOI: 10.4171/RLM/601

Published online: 2011-09-20

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

Fabrizio Catanese[1], Michael Lönne[2] and Fabio Perroni[3]

(1) Universität Bayreuth, Germany
(2) Universität Bayreuth, Germany
(3) Università degli Studi di Trieste, Italy

We show in this paper that the set of irreducible components of the family of Galois coverings of $\bP^1_{\bC}$ with Galois group isomorphic to $\Dn$ is in bijection with the set of possible numerical types. In this special case the numerical type is the equivalence class (for automorphisms of $\Dn$) of the function which to each conjugacy class $\sC$ in $\Dn$ associates the number of branch points whose local monodromy lies in the class $\sC$.

Keywords: Moduli spaces of curves, branched coverings of Riemann surfaces, Hurwitz equivalence, braid groups, monodromy

Catanese Fabrizio, Lönne Michael, Perroni Fabio: 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), 291-309. doi: 10.4171/RLM/601