The automorphism group of ${\overline{M}}_{g,n}$

Abstract

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

22 pages

References in corpus (2)

• Generating stable modular graphs
• Modular Compactifications of M_{1,n} II

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• The automorphism group of $M_{0,n}^{\text{trop}}$ and ${\overline{M}}_{0,n}^{\text{trop}}$
• On the automorphisms of Hassett's moduli spaces
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