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.
@article{bwmeta1.element.bwnjournal-article-apmv67z2p179bwm,
author = {G\'erard Gonzalez-Sprinberg and Monique Lejeune-Jalabert},
title = {Families of smooth curves on surface singularities and wedges},
journal = {Annales Polonici Mathematici},
volume = {66},
year = {1997},
pages = {179-190},
zbl = {0894.14017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv67z2p179bwm}
}
Gérard Gonzalez-Sprinberg; Monique Lejeune-Jalabert. Families of smooth curves on surface singularities and wedges. Annales Polonici Mathematici, Tome 66 (1997) pp. 179-190. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv67z2p179bwm/
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