Genus stabilization for moduli of curves with symmetries

Fabrizio Catanese; Michael Lönne; Fabio Perroni

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arXiv · 1301.4409

Genus stabilization for moduli of curves with symmetries

Fabrizio Catanese·Michael Lönne·Fabio Perroni

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Abstract

In a previous paper, arXiv:1206.5498, we introduced a new homological invariant $\e$ for the faithful action of a finite group G on an algebraic curve. We show here that the moduli space of curves admitting a faithful action of a finite group G with a fixed homological invariant $\e$, if the genus g' of the quotient curve is sufficiently large, is irreducible (and non empty iff the class satisfies the condition which we define as 'admissibility'). In the unramified case, a similar result had been proven by Dunfield and Thurston using the classical invariant in the second homology group of G, H_2(G, \ZZ). We achieve our result showing that the stable classes are in bijection with the set of admissible classes $\e$.

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BibTeX RIS

Fabrizio Catanese, Michael Lönne, Fabio Perroni. 2013-01-18. Genus stabilization for moduli of curves with symmetries. https://arxiv.org/abs/1301.4409

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