Geodesic
A construction of the Deligne-Mumford orbifold
Journal of the European Mathematical Society, Tome 8 (2006) no. 4, pp. 611-699

Voir la notice de l'article provenant de la source EMS Press

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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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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