Subvarieties of the hyperelliptic moduli determined by group actions

T. Shaska

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arXiv · 1302.3974

Subvarieties of the hyperelliptic moduli determined by group actions

T. Shaska

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Abstract

Let $\mathcal H_g$ be the moduli space of genus $g$ hyperelliptic curves. In this note, we study the locus $\mathcal L$ in $\mathcal H_g$ of curves admitting a $G$-action of given ramification type $\sigma$ 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 $\mathcal L$. The proof of the results is based solely on representations of finite subgroups of $PGL_2 (\mathbb C)$ and the Riemann-Hurwitz formula.

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BibTeX RIS

T. Shaska. 2013-02-16. Subvarieties of the hyperelliptic moduli determined by group actions. https://arxiv.org/abs/1302.3974

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