© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1983, tous droits réservés. L'accès aux archives de la revue « Annales scientifiques de l'É.N.S. » (http://www. elsevier.com/locate/ansens) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

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Following the study of the arc structure of singularities, initiated by J. Nash, we give criteria for the existence of smooth curves on a surface singularity (S, O) and of smooth branches of its generic hypersurface section. The main applications are the following: the existence of a natural partition of the set of smooth curves on (S, O) into families, a description of each of them by means of chains of infinitely near points and their associated maximal cycle and the existence of smooth curves on any sandwiched surface singularity. A wedge centered at a smooth curve on (S, O) is essentially a one-parameter deformation of the parametrization of the curve. We show that there is no wedge centered at smooth curves of two different families.

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We describe the group structure of monomial Cremona transformations. It follows that every element of this group is a product of quadratic monomial transformations, and geometric descriptions in terms of fans.