Geodesic
Subvarieties of the Hyperelliptic Moduli Determined by Group Actions
Serdica Mathematical Journal, Tome 32 (2006) no. 4, pp. 355-374.

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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.
Keywords: Hyperelliptic Curves, Automorphism Groups 
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     author = {Shaska, T.},
     title = {Subvarieties of the {Hyperelliptic} {Moduli} {Determined} by {Group} {Actions}},
     journal = {Serdica Mathematical Journal},
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     url = {http://geodesic.mathdoc.fr/item/SMJ2_2006_32_4_a4/}
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Shaska, T. Subvarieties of the Hyperelliptic Moduli Determined by Group Actions. Serdica Mathematical Journal, Tome 32 (2006) no. 4, pp. 355-374. http://geodesic.mathdoc.fr/item/SMJ2_2006_32_4_a4/