The Automorphisms group of \bar{M}_{g,n}

Details The Automorphisms group of \bar{M}_{g,n} The Automorphisms group of \bar{M}_{g,n}

2011-10-07

arxiv.org/abs/1110.1464v1

Mathematics

Algebraic Geometry

22 pages

Scientific paper

Let \bar{\mathcal{M}}_{g,n}$ be the moduli stack parametrizing Deligne-Mumford stable n-pointed genus g curves and let \bar{M}_{g,n} be its coarse moduli space: the Deligne-Mumford compactification of the moduli space of n-pointed genus g smooth curves. We prove that the automorphisms groups of \bar{\mathcal{M}}_{g,n} and \bar{M}_{g,n} are isomorphic to the symmetric group on n elements S_{n} for any g,n such that 2g-2+n\geq 3, and compute the remaining cases.

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