JournalsggdVol. 9, No. 4pp. 1185–1229

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

  • Fabrizio Catanese

    Universität Bayreuth, Germany
  • Michael Lönne

    Universität Bayreuth, Germany
  • Fabio Perroni

    Università degli Studi di Trieste, Italy
The irreducible components of the moduli space of dihedral covers of algebraic curves cover
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Abstract

The main purpose of this paper is to introduce a new invariant for the action of a finite group GG on a compact complex curve of genus gg. 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 DnD_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.

Cite this article

Fabrizio Catanese, Michael Lönne, Fabio Perroni, The irreducible components of the moduli space of dihedral covers of algebraic curves. Groups Geom. Dyn. 9 (2015), no. 4, pp. 1185–1229

DOI 10.4171/GGD/338