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

Abstract. 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 ofMg,n. We put an analytic structure on this quotient and prove that with respect to this structure, the compactifica-tion is canonically isomorphic (as an analytic space) to the Deligne-Mumford compactificationMg,n. Content