An Analytic Construction of the Deligne-mumford Compactification of the Moduli Space of Curves
نویسندگان
چکیده
In 1969, P. Deligne and D. Mumford compactified the moduli space of curves Mg,n. Their compactification Mg,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 Mg,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 Mg,n.
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