On the automorphisms of moduli spaces of curves
Alex Massarenti, Massimiliano Mella

TL;DR
This paper surveys recent results on automorphisms of moduli spaces of curves, extending techniques to intermediate and degenerate cases, providing a comprehensive overview of the automorphism groups in these geometric contexts.
Contribution
It extends previous work on automorphisms of moduli spaces to include intermediate and degenerate cases, broadening understanding of their symmetries.
Findings
Automorphism groups of various moduli spaces are characterized.
Techniques are extended to spaces with zero weights.
Results unify understanding of automorphisms across different moduli space compactifications.
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 , and to the degenerations of Hassett's spaces obtained by allowing zero weights.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry
