nLab 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

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