Families of smooth curves on surface singularities and wedges

• Autorzy: Gérard Gonzalez-Sprinberg , Monique Lejeune-Jalabert
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

surface singularities; smooth curves; maximal cycle; wedges

Kategorie tematyczne

• 14E15: Global theory and resolution of singularities
• 14B05: Singularities

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 67
• Numer: 2
• Strony: 179-190

Daty

wydano

1997

otrzymano

1996-10-17

Twórcy

autor

Gérard Gonzalez-Sprinberg

• 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)

autor

Monique Lejeune-Jalabert

• 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)

Bibliografia

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