The main purpose of this paper is to introduce a new invariant for the action of a finite group on a compact complex curve of genus . 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 . This invariant has later been used in  where the results of Livingston  and of Dunfield and Thurston  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. 1185–1229DOI 10.4171/GGD/338