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Families of smooth curves on surface singularities and wedges

Gérard Gonzalez-SprinbergMonique Lejeune-Jalabert — 1997

Annales Polonici Mathematici

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...

The Denef-Loeser series for toric surface singularities.

Monique Lejeune-JalabertAna J. Reguera — 2003

Revista Matemática Iberoamericana

Let H denote the set of formal ares going through a singular point of an algebraic variety V defined over an algebraically closed field k of charactcristic zcro. In the late sixties, J, Nash has observed that for any nonnegative integer s, the set js(H) of s-jets of ares in H is a constructible subset of some affine space. Recently (1999), J. Denef and F. Loeser have proved that the Poincaré series associated with the image of js(H) in some suitable localization of the Grothendieck ring of algebraic...

Clôture intégrale des idéaux et équisingularité

Monique Lejeune-JalabertBernard Teissier — 2008

Annales de la faculté des sciences de Toulouse Mathématiques

This text has two parts. The first one is the essentially unmodified text of our 1973-74 seminar on integral dependence in complex analytic geometry at the Ecole Polytechnique with J-J. Risler’s appendix on the Łojasiewicz exponents in the real-analytic framework. The second part is a short survey of more recent results directly related to the content of the seminar. The first part begins with the definition and elementary properties of the ν ¯ order function associated to an ideal I of...

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