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Families of smooth curves on surface singularities and wedges

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Gonzalez-Sprinberg G., Lejeune-Jalabert M.

Annales Polonici Mathematici

1997

tom 67

nr 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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Gonzalez-Sprinberg G.

1 Lejeune-Jalabert M.

1 1997

Wyniki wyszukiwania

Families of smooth curves on surface singularities and wedges