Abstract
In a previous paper, (CLP12), we introduced a new homological invariant for the faithful action of a nite group G on an algebraic curve. We show here that the moduli space of curves admitting a faithful action of a nite group G with a xed homological invariant , if the genus g 0 of the quotient curve satises g 0 >> 0, is irreducible (and non empty i the class satises the 'admissibility' condition). We achieve this by showing that the stable classes are in bijection with the set of admissible classes .
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