Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 32, No 4, (2006), 355p-374p
Let Hg be the moduli space of genus g hyperelliptic curves. In this note, we study the locus Hg (G,σ) in Hg of curves admitting a G-action of given ramification type σ and inclusions between such loci. For each genus we determine the list of all possible groups, the inclusions among the loci, and the corresponding equations of the generic curve in Hg (G, σ). The proof of the results is based solely on representations of finite subgroups of PGL2 (C) and the Riemann-Hurwitz formula.