Geodesic
The irreducible components of the moduli space of dihedral covers of algebraic curves
Fabrizio Catanese1 ; Michael Lönne1 ; Fabio Perroni2
1Universität Bayreuth, Germany
2Università degli Studi di Trieste, Italy
Groups, geometry, and dynamics, Tome 9 (2015) no. 4, pp. 1185-1229

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DOI

The main purpose of this paper is to introduce a new invariant for the action of a finite group G on a compact complex curve of genus g. With the aid of this invariant we achieve the classication of the components of the locus (in the moduli space) of curves admitting an effective action by the dihedral group Dn​. This invariant has later been used in [11] where the results of Livingston [29] and of Dunfield and Thurston [17] have been extended to the ramified case.
DOI : 10.4171/ggd/338
Classification : 14-XX, 20-XX
Mots-clés : Algebraic curves, topological type of coverings, monodromy, Hurwitz spaces, Hurwitz vectors, dihedral group, homological invariant, moduli space of curves, curves with automorphisms, mapping class group

Fabrizio Catanese  1   ; Michael Lönne  1   ; Fabio Perroni  2

1 Universität Bayreuth, Germany
2 Università degli Studi di Trieste, Italy 
Fabrizio Catanese; Michael Lönne; Fabio Perroni. The irreducible components of the moduli space of dihedral covers of algebraic curves. Groups, geometry, and dynamics, Tome 9 (2015) no. 4, pp. 1185-1229. doi: 10.4171/ggd/338
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     title = {The irreducible components of the moduli space of dihedral covers of algebraic curves},
     journal = {Groups, geometry, and dynamics},
     pages = {1185--1229},
     year = {2015},
     volume = {9},
     number = {4},
     doi = {10.4171/ggd/338},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/338/}
}
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