Families of smooth curves on surface singularities and wedges

Volume 67 / 1997

Gérard Gonzalez-Sprinberg, Monique Lejeune-Jalabert Annales Polonici Mathematici 67 (1997), 179-190 DOI: 10.4064/ap-67-2-179-190


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.


  • Gérard Gonzalez-Sprinberg
  • Monique Lejeune-Jalabert

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