A propos du problème des arcs de Nash

Plénat, Camille

doi:10.5802/aif.2115

Cited by 16 publications

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“…On the other hand, bijectivity of the Nash mapping has been shown for many classes of surfaces (see [6], [10], [8], [9], [12], [13], [17], [19], [20], [21], [22], [24], [25], [26]). The techniques leading to the proof of each of these cases are different in nature, and the proofs are often complicated.…”

Section: Introductionmentioning

confidence: 99%

The Nash problem for surfaces

Bobadilla

Pereira

2012

Ann. Math.

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Section: Introductionmentioning

confidence: 99%

The Nash problem for surfaces

Bobadilla

Pereira

2012

Ann. Math.

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“…As an immediate consequence of Proposition of Plenat [10] and my Theorem [8] we have: • (N N ) is true for any subgraph of Γ.…”

Section: It Follows From the Previous Item That Ifmentioning

confidence: 99%

“…Among the principal contributions to this subject we can cite Monique Lejeune-Jalabert [6], [7], Ana Reguera [7], [13], [14], S. Ishii and J. Kollar [5], G. Gonzalez-Sprinberg and Monique Lejeune-Jalabert [4], Camille Plenat [10] and C. Plenat and P. Popescu-Pampu [12]. The study of arcs spaces was further developed by Kontsevich, Denef and Loeser [1] in the theory of motivic integration.…”

Section: §1 Introductionmentioning

confidence: 99%

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Some Numerical Criteria for the Nash Problem on Arcs for Surfaces

Morales

2008

Nagoya Mathematical Journal

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Abstract. Let (X, O) be a germ of a normal surface singularity, π :X → X be the minimal resolution of singularities and let A = (ai,j) be the n × n symmetrical intersection matrix of the exceptional set ofX. In an old preprint Nash proves that the set of arcs on a surface singularity is a scheme H, and defines a map N from the set of irreducible components of H to the set of exceptional components of the minimal resolution of singularities of (X, O).

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“…[6]) et qui (dans le cas des singularités rationnelles) permet d'ordonner partiellement les familles d'arcs.…”

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Résolution du problème des arcs de Nash pour les points doubles rationnels Dn

Plénat

2005

Comptes Rendus. Mathématique

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Reçu le 24 janvier 2005 ; accepté après révision le 13 avril 2005Présenté par Jean-Pierre Demailly RésuméCette Note a pour objet le problème des arcs de Nash, selon lequel il y aurait autant de familles d'arcs sur un germe de surface singulier U que de composantes essentielles d'une désingularisation de cette singularité. On résout le problème par l'affirmative pour les points doubles rationnels D n (n 4). Pour citer cet article : C. Plénat, C. R. Acad. Sci. Paris, Ser. I 340 (2005).  2005 Académie des sciences. Publié par Elsevier SAS. Tous droits réservés. AbstractA solution to the Nash problem of arcs for rational double points D n . This Note 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. We prove that this claim holds for the rational double points D n (n 4). To cite this article: C. Plénat, C. R. Acad. Sci. Paris, Ser. I 340 (2005).  2005 Académie des sciences. Publié par Elsevier SAS. Tous droits réservés.

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A propos du problème des arcs de Nash

Cited by 16 publications

References 0 publications

The Nash problem for surfaces

The Nash problem for surfaces

Some Numerical Criteria for the Nash Problem on Arcs for Surfaces

Résolution du problème des arcs de Nash pour les points doubles rationnels Dn

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