nLab Deligne-Mumford compactification

Idea

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.

Related concepts

• augmented Teichmüller space

• Deligne-Mumford stack

References

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

• pdf

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)