Moduli Stacks of Permutation Classes of Pointed Stable Curves

The notion of m/Gamma-pointed stable curves is introduced. It should be viewed as a generalization of the notion of m-pointed stable curves of a given genus, where the labels of the marked points are only determined up to the action of a group of permutations G. The classical moduli spaces and moduli stacks are generalized to this wider setting. Finally, an explicit construction of the new moduli stack of m/Gamma-pointed stable curves as a quotient stack is given.