Moduli stacks of permutation classes of pointed stable curves

Details Moduli stacks of permutation classes of pointed stable curves Moduli stacks of permutation classes of pointed stable curves

2006-11-22

arxiv.org/abs/math/0611710v1

Mathematics

Algebraic Geometry

21 pages

Scientific paper

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 $\Gamma$. 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.

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