In this paper we introduce a new invariant for the action of a finite group $G$ on a compact comp... more In this paper we 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 classification of the components of the locus (in the moduli space) of curves admitting an effective action by the dihedral group $D_n$. This invariant could be useful in order to extend the results of Livingston and Dunfield and Thurston to the ramified case.
In this paper we introduce a new invariant for the action of a finite group $G$ on a compact comp... more In this paper we 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 classification of the components of the locus (in the moduli space) of curves admitting an effective action by the dihedral group $D_n$. This invariant could be useful in order to extend the results of Livingston and Dunfield and Thurston to the ramified case.
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Papers by Michael Loenne