Title | Genus stabilization for moduli of curves with symmetries |

Publication Type | Journal Article |

Year of Publication | 2013 |

Authors | Catanese, F, Lönne, M, Perroni, F |

Keywords | group actions; mapping class group; Moduli space of curves; Teichmüller space |

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

URL | http://hdl.handle.net/1963/6509 |

## Genus stabilization for moduli of curves with symmetries

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