Deligne-Mumford compactification

A standard compactification due to (Deligne-Mumford 69) of a moduli stack of curves by including curves with singularities,in particular by including nodal curves.

The original article is

- Pierre Deligne, David Mumford,
*The irreducibility of the space of curves of given genus*, Publications Mathématiques de l’IHÉS (Paris) 36: 75–109 (1969) numdam

Reviews include

Discussion over the complex numbers showing that the DM-compactification here is equivalently the orbifold quotient of augmented Teichmüller space by the mapping class group is in

- John Hubbard, Sarah Koch,
*An analytic construction of the Deligne-Mumford compactification of the moduli space of curves*(arXiv:1301.0062)