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ArticleOriginal scientific text

Title

Families of smooth curves on surface singularities and wedges

Authors 1, 1

Affiliations

  1. Université de Grenoble I, Institut Fourier, UMR 5582 du CNRS et de l'UJF, UFR de Mathématiques, B.P. 74, 38402 St. Martin d'Hères Cedex (France)

Abstract

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.

Keywords

ENG
surface singularities, smooth curves, maximal cycle, wedges

Bibliography

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Annales Polonici Mathematici
1997/67/2
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Pages:
179-190
Main language of publication
English
Received
1996-10-17
Published
1997
Exact and natural sciences