Let the canonical decomposition of the space of arcs passing through a normal surface singularity. In this paper, we give two new conditions to ensure that is not included in . These conditions allow us to give two different direct demonstration of Nah problem for minimal sandwiched singularities.
Soit 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’est pas inclus dans . On applique ces conditions pour donner deux nouvelles preuves du problème de Nash pour les singularités sandwich minimales.
Classification: 14J17
Keywords: geometry algebraic, space of arcs, minimal sandwiched singularities, problem of Nash
@article{AIF_2005__55_3_805_0, author = {Pl\'enat, Camille}, title = {A propos du probl\`eme des arcs de {Nash}}, journal = {Annales de l'Institut Fourier}, pages = {805--823}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {3}, year = {2005}, doi = {10.5802/aif.2115}, mrnumber = {2149404}, zbl = {1080.14021}, language = {fr}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2115/} }
TY - JOUR TI - A propos du problème des arcs de Nash JO - Annales de l'Institut Fourier PY - 2005 DA - 2005/// SP - 805 EP - 823 VL - 55 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2115/ UR - https://www.ams.org/mathscinet-getitem?mr=2149404 UR - https://zbmath.org/?q=an%3A1080.14021 UR - https://doi.org/10.5802/aif.2115 DO - 10.5802/aif.2115 LA - fr ID - AIF_2005__55_3_805_0 ER -
Plénat, Camille. A propos du problème des arcs de Nash. Annales de l'Institut Fourier, Volume 55 (2005) no. 3, pp. 805-823. doi : 10.5802/aif.2115. https://aif.centre-mersenne.org/articles/10.5802/aif.2115/
[Ar] On isolated rational singularities of surfaces, Amer. J. Math., Tome 88 (1966), pp. 129-136 | Article | MR: 199191 | Zbl: 0142.18602
[Fe] Equivalence of the Nash conjecture for primitive and sandwiched singularities, Proc. Amer. Math. Soc., Tome 133 (2005), pp. 677-679 | Article | MR: 2113914 | Zbl: 1056.14004
[IK] The Nash problem on arc families of singularities, Duke Math. J., Tome 120 (2003), pp. 601-620 | Article | MR: 2030097 | Zbl: 1052.14011
[La] Taut two-dimensional singularities, Math. Ann., Tome 205 (1973), pp. 131-164 | Article | EuDML: 162485 | MR: 333238 | Zbl: 0281.32010
[Le] Courbes tracées sur un germe d'hypersurface, Amer. J. Math., Tome 112 (1990), pp. 525-568 | Article | MR: 1064990 | Zbl: 0743.14002
[Na] Arc structure of singularities, A celebration of John F. Nash, Jr., Duke Math. J., Tome 81 (1995) no. 1, pp. 31-38 | MR: 1381967 | Zbl: 0880.14010
[Re] Families of arcs on rational surface singularities, Manuscripta Math., Tome 88 (1995) no. 3, pp. 321-333 | EuDML: 156131 | MR: 1359701 | Zbl: 0867.14012
[Sp1] Sandwiched singularities and desingularization of surfaces by normalized Nash transformations, Annals of Math., Tome 131 (1990), pp. 411-491 | Article | MR: 1053487 | Zbl: 0719.14005
[Sp2] Valuation in function fields of surfaces, Amer. J. Math., Tome 112 (1990), pp. 107-156 | Article | MR: 1037606 | Zbl: 0716.13003
Cited by Sources: