@article {2013,
title = {Genus stabilization for moduli of curves with symmetries},
number = {arXiv:1301.4409;},
year = {2013},
note = {21 pages, 2 figures},
publisher = {SISSA},
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 $\\e$.},
keywords = {group actions, mapping class group, Moduli space of curves, Teichm{\"u}ller space},
url = {http://hdl.handle.net/1963/6509},
author = {Fabrizio Catanese and Michael L{\"o}nne and Fabio Perroni}
}