AN ANALYTIC CONSTRUCTION OF THE DELIGNE-MUMFORD COMPACTIFICATION OF THE MODULI SPACE OF CURVES

In 1969, P. Deligne and D. Mumford compactified the moduli space of curves M-g,M-n. Their compactification (M) over bar (g,n) is a projective algebraic variety, and as such it has an underlying analytic structure. Alternatively, the quotient of the augmented Teichmuiller space by the action of the mapping class group gives a compactification of M-g,M-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 (M) over bar (g,n).