2014
DOI: 10.1007/978-3-319-05681-4_9
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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 M 0,n, and to the degenerations of Hassett's spaces obtained by allowing zero weights.

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Cited by 6 publications
(2 citation statements)
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“…Now, applying the techniques developed in [7, 17, 18, 34, 35, 37, 38] to deal with automorphisms of moduli spaces of curves and stable maps and in [2, 3] for moduli of parabolic vector bundles, we will finally compute the pseudo‐automorphism group of the spaces of complete forms. We will need the following preliminary result.…”
Section: Pseudo‐automorphismsmentioning
confidence: 99%
“…Now, applying the techniques developed in [7, 17, 18, 34, 35, 37, 38] to deal with automorphisms of moduli spaces of curves and stable maps and in [2, 3] for moduli of parabolic vector bundles, we will finally compute the pseudo‐automorphism group of the spaces of complete forms. We will need the following preliminary result.…”
Section: Pseudo‐automorphismsmentioning
confidence: 99%
“…It is a corollary of some known results. If W is a weak del Pezzo surface, then W is log Fano (see, e.g., [33, Proposition 2.6]). Hence, by the cone theorem [26, Theorem 3.7], its nef cone is a rational polyhedral cone spanned by classes of semiample divisors.…”
mentioning
confidence: 99%