01314nas a2200181 4500008004100000245006100041210006100102260001000163520076900173653001800942653002400960653002700984653002301011100002301034700002001057700001901077856003601096 2013 en d00aGenus stabilization for moduli of curves with symmetries0 aGenus stabilization for moduli of curves with symmetries bSISSA3 aIn 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 $\\e$.10agroup actions10amapping class group10aModuli space of curves10aTeichmüller space1 aCatanese, Fabrizio1 aLönne, Michael1 aPerroni, Fabio uhttp://hdl.handle.net/1963/6509