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October 2014 An analytic construction of the Deligne-Mumford compactification of the moduli space of curves
John H. Hubbard, Sarah Koch
J. Differential Geom. 98(2): 261-313 (October 2014). DOI: 10.4310/jdg/1406552251

Abstract

In 1969, P. Deligne and D. Mumford compactified the moduli space of curves $\mathcal{M}_{g,n}$. Their compactification $\overline{\mathcal{M}}_{g,n}$ is a projective algebraic variety, and as such it has an underlying analytic structure. Alternatively, the quotient of the augmented Teichmüller space by the action of the mapping class group gives a compactification of $\mathcal{M}_{g,n}$. We put an analytic structure on this quotient and prove that with respect to this structure, the compactification is canonically isomorphic (as an analytic space) to the Deligne-Mumford compactification $\overline{\mathcal{M}}_{g,n}$.

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John H. Hubbard. Sarah Koch. "An analytic construction of the Deligne-Mumford compactification of the moduli space of curves." J. Differential Geom. 98 (2) 261 - 313, October 2014. https://doi.org/10.4310/jdg/1406552251

Information

Published: October 2014
First available in Project Euclid: 28 July 2014

zbMATH: 1318.32019
MathSciNet: MR3263519
Digital Object Identifier: 10.4310/jdg/1406552251

Rights: Copyright © 2014 Lehigh University

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Vol.98 • No. 2 • October 2014
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