Résolution de Nash des points doubles rationnels
Annales de l'Institut Fourier, Tome 32 (1982) no. 2, pp. 111-178.

Nous présentons une méthode qui permet de calculer le transformée de Nash (et sa normalisation) d’une singularité de surface pour laquelle on dispose d’une résolution explicite. Comme exemple nous calculons la résolution des points doubles rationnels obtenue par itération du transformé de Nash normalisé.

We give a method for computing the Nash transform (and its normalization) of a surface singularity for which one has an explicit resolution. As an example we compute the resolution of the rational double points obtained by iteration of the Nash transform normalized.

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     author = {Gonzalez-Sprinberg, Gerardo},
     title = {R\'esolution de {Nash} des points doubles rationnels},
     journal = {Annales de l'Institut Fourier},
     pages = {111--178},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {32},
     number = {2},
     year = {1982},
     doi = {10.5802/aif.874},
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Gonzalez-Sprinberg, Gerardo. Résolution de Nash des points doubles rationnels. Annales de l'Institut Fourier, Tome 32 (1982) no. 2, pp. 111-178. doi : 10.5802/aif.874. http://archive.numdam.org/articles/10.5802/aif.874/

[1] S. Abhyankar, Quasi rational singularities, Am. J. of Math., 101 (1979), 267-300. | MR | Zbl

[2] M. Artin, On isolated rational singularities of surfaces, Amer. J. Math., 88 (1966), 129-136. | MR | Zbl

[3] M. Artin, Some numerical criteria for contractability of curves on algebraic surfaces, Amer. J. Math., 84 (1962), 485-496. | MR | Zbl

[4] E. Brieskorn, Rationale singularitäten komplexer Flächen, Inv. Math., 4 (1968), 336-358. | MR | Zbl

[5] A. Grothendieck, Éléments de Géométrie Algébrique I, 1.9.8.4 Springer (1971). | MR | Zbl

[6] G. González-Sprinberg, Éventails en dimension 2 et transformé de Nash, Publications de l'E.N.S., Paris (1977).

[7] F. Hirzebruch, Uber vierdimensionale Riemannsche Flächen mehrdeutiger analytischer Funktionen von zwei komplexen Verändlichen, Math. Ann., 126 (1953), 1-22. | MR | Zbl

[8] F. Klein, The Icosahedron and the General 5th Degree Equation, 1884, Dover reprint, 1956.

[9] H. Laufer, Deformations of resolutions of two-dimensional singularities, Proc. of Rice conference on Complex Analysis (1972). | Zbl

[10] H. Laufer, Taut two dimensional singularities, Math. Ann., 205 (1973), 131-164. | EuDML | MR | Zbl

[11] J. Lipman, Rational singularities with applications to algebraic surfaces and unique factorizations, Publ. Math. I.H.E.S., 36 (1969), 195-279. | EuDML | Numdam | MR | Zbl

[12] H. Pinkham, Singularités rationnelles de surfaces, Springer Lecture Notes, n° 777 (1980). | MR | Zbl

[13] O. Riemenschneider, Deformationen von Quotientensingularitäten (nach zyklischen Gruppen), Math. Ann., 209 (1974), 211-248. | EuDML | MR | Zbl

[14] Kempf, Knudsen, Mumford et Saint-Donat, Toroidal Embeddings I, Springer Lecture Notes, n° 339 (1973). | MR | Zbl

[15] G. N. Tyurina, Absolute isolatedness of rational singularities and triple rational points, Func. Anal. Appl., 2 (1968), 324-332. | Zbl

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