%0 Journal Article
%D 2013
%T Genus stabilization for moduli of curves with symmetries
%A Fabrizio Catanese
%A Michael Lönne
%A Fabio Perroni
%K group actions
%K mapping class group
%K Moduli space of curves
%K Teichmüller space
%X 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 $\\e$.
%I SISSA
%G en
%U http://hdl.handle.net/1963/6509
%1 6461
%2 Mathematics
%4 1
%# MAT/03 GEOMETRIA
%$ Submitted by Fabio Perroni (perroni@sissa.it) on 2013-02-27T21:38:16Z\nNo. of bitstreams: 1\n1301.4409v1.pdf: 515958 bytes, checksum: 378f14240b070b5bc840d1cd9ca8e6a0 (MD5)