## Journal of Differential Geometry

### An analytic construction of the Deligne-Mumford compactification of the moduli space of curves

#### 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 $\overline{\mathcal{M}}_{g,n}$.

#### Article information

Source
J. Differential Geom., Volume 98, Number 2 (2014), 261-313.

Dates
First available in Project Euclid: 28 July 2014

https://projecteuclid.org/euclid.jdg/1406552251

Digital Object Identifier
doi:10.4310/jdg/1406552251

Mathematical Reviews number (MathSciNet)
MR3263519

Zentralblatt MATH identifier
1318.32019

#### Citation

Hubbard, John H.; Koch, Sarah. An analytic construction of the Deligne-Mumford compactification of the moduli space of curves. J. Differential Geom. 98 (2014), no. 2, 261--313. doi:10.4310/jdg/1406552251. https://projecteuclid.org/euclid.jdg/1406552251