On the automorphisms of moduli spaces of curves

Abstract

In the last years the biregular automorphisms of the Deligne-Mumford's and Hassett's compactifications of the moduli space of n-pointed genus g smooth curves have been extensively studied by A. Bruno and the authors. In this paper we give a survey of these recent results and extend our techniques to some moduli spaces appearing as intermediate steps of the Kapranov's and Keel's realizations of ${\bar{M}}_{0,n}$, and to the degenerations of Hassett's spaces obtained by allowing zero weights.

arXiv comment15 pages. The material of version 1 has been reorganized and expanded in this paper and in arXiv:1307.6828 on automorphisms of Hassett's moduli spaces