Geodesic
Families of smooth curves on surface singularities and wedges
Annales Polonici Mathematici, Tome 67 (1997) no. 2, pp. 179-190.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ap-67-2-179-190
Keywords: surface singularities, smooth curves, maximal cycle, wedges

Gérard Gonzalez-Sprinberg 1 ; Monique Lejeune-Jalabert 1

1 
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Gérard Gonzalez-Sprinberg; Monique Lejeune-Jalabert. Families of smooth curves on surface singularities and wedges. Annales Polonici Mathematici, Tome 67 (1997) no. 2, pp. 179-190. doi : 10.4064/ap-67-2-179-190. http://geodesic.mathdoc.fr/articles/10.4064/ap-67-2-179-190/

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