2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100806We define the Deligne Mumford orbifold axiomatically by a universal mapping property, show that this universal mapping property is equivalent to an infinitessimal universal mapping property, and use the latter to give an existence proof.78 pages. See also http://www.math.ethz.ch/~salamon/ and http://www.math.wisc.edu/~robbin. Submitted to JEMS. Revised October 2005Symplectic GeometryAlgebraic Geometry32G15text