Geodesic
A construction of the Deligne-Mumford orbifold
Journal of the European Mathematical Society, Tome 8 (2006) no. 4, pp. 611-699 Cet article a éte moissonné depuis la source EMS Press

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The Deligne–Mumford moduli space is the space Mg,n​ of isomorphism classes of stable nodal Riemann surfaces of arithmetic genus g with n marked points. A marked nodal Riemann surface is stable if and only if its isomorphism group is finite. We introduce the notion of a universal unfolding of a marked nodal Riemann surface and show that it exists if and only if the surface is stable. A natural construction based on the existence of universal unfoldings endows the Deligne–Mumford moduli space with an orbifold structure. We include a proof of compactness. Our proofs use the methods of differential geometry rather than algebraic geometry.
DOI : 10.4171/jems/69
Classification : 58-XX, 00-XX
Keywords: Stable curves, Teichmüller theory, Deligne-Mumford orbifolds 
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     author = {Joel W. Robbin and Dietmar A. Salamon},
     title = {A construction of the {Deligne-Mumford} orbifold},
     journal = {Journal of the European Mathematical Society},
     pages = {611--699},
     year = {2006},
     volume = {8},
     number = {4},
     doi = {10.4171/jems/69},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/69/}
}
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Joel W. Robbin; Dietmar A. Salamon. A construction of the Deligne-Mumford orbifold. Journal of the European Mathematical Society, Tome 8 (2006) no. 4, pp. 611-699. doi: 10.4171/jems/69

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