Currently displaying 1 – 3 of 3

Showing per page

Order by Relevance | Title | Year of publication

A propos du problème des arcs de Nash

Camille Plénat — 2005

Annales de l’institut Fourier

Soit = N i la décomposition canonique de l’espace des arcs passant par une singularité normale de surface. Dans cet article, on propose deux nouvelles conditions qui si elles sont vérifiées permettent de montrer que N i n’est pas inclus dans N j . On applique ces conditions pour donner deux nouvelles preuves du problème de Nash pour les singularités sandwich minimales.

The Nash problem of arcs and the rational double points D n

Camille Plénat — 2008

Annales de l’institut Fourier

This paper deals with the Nash problem, which consists in comparing the number of families of arcs on a singular germ of surface U with the number of essential components of the exceptional divisor in the minimal resolution of this singularity. We prove their equality in the case of the rational double points D n ( n 4 ).

A class of non-rational surface singularities with bijective Nash map

Camille PlénatPatrick Popescu-Pampu — 2006

Bulletin de la Société Mathématique de France

Let ( 𝒮 , 0 ) be a germ of complex analytic normal surface. On its minimal resolution, we consider the reduced exceptional divisor E and its irreducible components E i , i I . The Nash map associates to each irreducible component C k of the space of arcs through 0 on 𝒮 the unique component of E cut by the strict transform of the generic arc in C k . Nash proved its injectivity and asked if it was bijective. As a particular case of our main theorem, we prove that this is the case if E · E i < 0 for any  i I .

Page 1

Download Results (CSV)