A propos de la conjecture de Nash

Camille Plenat (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

This paper deals with the Nash problem, which claims that there are as many families of arcs on a singular germ of surface $U$ as there are essential components of the exceptional divisor in the desingularisation of this singularity. Let $\mathcal{H}=\bigcup \bar{N_\alpha}$ be a particular decomposition of the set of arcs on $U$, described later on. We give two new conditions to insure that $\bar{N_\alpha}\not \subset \bar{N_\beta}$, $\alpha \not = \beta$; more precisely,for the first one, we claim that if there exists $f \in {\mathcal{O}}_{U}$ such that $ord_{E_\alpha}(f)

Domaines: Géométrie algébrique [math.AG]; Algèbre commutative [math.AC]

Camille Plenat. A propos de la conjecture de Nash. Annales de l'Institut Fourier, 2005, 3 (55), p 805-823. ⟨hal-00966621⟩