Groups, Geometry, and Dynamics


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Volume 9, Issue 4, 2015, pp. 1185–1229
DOI: 10.4171/GGD/338

Published online: 2015-11-16

The irreducible components of the moduli space of dihedral covers of algebraic curves

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

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 $D_n$. 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.

Keywords: 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

Catanese Fabrizio, Lönne Michael, Perroni Fabio: The irreducible components of the moduli space of dihedral covers of algebraic curves. Groups Geom. Dyn. 9 (2015), 1185-1229. doi: 10.4171/GGD/338