TY - JOUR
T1 - Genus stabilization for moduli of curves with symmetries
Y1 - 2013
A1 - Fabrizio Catanese
A1 - Michael Lönne
A1 - Fabio Perroni
KW - group actions
KW - mapping class group
KW - Moduli space of curves
KW - Teichmüller space
AB - 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 $\\e$.
PB - SISSA
UR - http://hdl.handle.net/1963/6509
N1 - 21 pages, 2 figures
U1 - 6461
U2 - Mathematics
U4 - 1
U5 - MAT/03 GEOMETRIA
ER -