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

By John H. Hubbard, Sarah Koch. 2013

65 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/4adb7921a00fceb1038d599d368d366cfda3cab0

Citations in the corpus

• Kähler–Einstein Metrics on Stable Varieties and log Canonical Pairs (2013, unknown): “Further, this condition was known for a long time to be equivalent to the other ones in the one dimensional case already, see e.g. [ HK14 , § 1].”