Résolution de Nash des points doubles rationnels

Gerardo Gonzalez-Sprinberg

Annales de l'institut Fourier (1982)

  • Volume: 32, Issue: 2, page 111-178
  • ISSN: 0373-0956

Abstract

top
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.

How to cite

top

Gonzalez-Sprinberg, Gerardo. "Résolution de Nash des points doubles rationnels." Annales de l'institut Fourier 32.2 (1982): 111-178. <http://eudml.org/doc/74533>.

@article{Gonzalez1982,
abstract = {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.},
author = {Gonzalez-Sprinberg, Gerardo},
journal = {Annales de l'institut Fourier},
keywords = {Nash transform; surface singularity; resolution},
language = {fre},
number = {2},
pages = {111-178},
publisher = {Association des Annales de l'Institut Fourier},
title = {Résolution de Nash des points doubles rationnels},
url = {http://eudml.org/doc/74533},
volume = {32},
year = {1982},
}

TY - JOUR
AU - Gonzalez-Sprinberg, Gerardo
TI - Résolution de Nash des points doubles rationnels
JO - Annales de l'institut Fourier
PY - 1982
PB - Association des Annales de l'Institut Fourier
VL - 32
IS - 2
SP - 111
EP - 178
AB - 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.
LA - fre
KW - Nash transform; surface singularity; resolution
UR - http://eudml.org/doc/74533
ER -

References

top
  1. [1] S. ABHYANKAR, Quasi rational singularities, Am. J. of Math., 101 (1979), 267-300. Zbl0425.14009MR80h:14014
  2. [2] M. ARTIN, On isolated rational singularities of surfaces, Amer. J. Math., 88 (1966), 129-136. Zbl0142.18602MR33 #7340
  3. [3] M. ARTIN, Some numerical criteria for contractability of curves on algebraic surfaces, Amer. J. Math., 84 (1962), 485-496. Zbl0105.14404MR26 #3704
  4. [4] E. BRIESKORN, Rationale singularitäten komplexer Flächen, Inv. Math., 4 (1968), 336-358. Zbl0219.14003MR36 #5136
  5. [5] A. GROTHENDIECK, Éléments de Géométrie Algébrique I, 1.9.8.4 Springer (1971). Zbl0203.23301MR50 #7129
  6. [6] G. GONZÁLEZ-SPRINBERG, Éventails en dimension 2 et transformé de Nash, Publications de l'E.N.S., Paris (1977). Zbl0349.14005
  7. [7] F. HIRZEBRUCH, Uber vierdimensionale Riemannsche Flächen mehrdeutiger analytischer Funktionen von zwei komplexen Verändlichen, Math. Ann., 126 (1953), 1-22. Zbl0093.27605MR16,26d
  8. [8] F. KLEIN, The Icosahedron and the General 5th Degree Equation, 1884, Dover reprint, 1956. 
  9. [9] H. LAUFER, Deformations of resolutions of two-dimensional singularities, Proc. of Rice conference on Complex Analysis (1972). Zbl0281.32009
  10. [10] H. LAUFER, Taut two dimensional singularities, Math. Ann., 205 (1973), 131-164. Zbl0281.32010MR48 #11563
  11. [11] J. LIPMAN, Rational singularities with applications to algebraic surfaces and unique factorizations, Publ. Math. I.H.E.S., 36 (1969), 195-279. Zbl0181.48903MR43 #1986
  12. [12] H. PINKHAM, Singularités rationnelles de surfaces, Springer Lecture Notes, n° 777 (1980). Zbl0459.14009MR82d:14021
  13. [13] O. RIEMENSCHNEIDER, Deformationen von Quotientensingularitäten (nach zyklischen Gruppen), Math. Ann., 209 (1974), 211-248. Zbl0275.32010MR51 #3518
  14. [14] KEMPF, KNUDSEN, MUMFORD et SAINT-DONAT, Toroidal Embeddings I, Springer Lecture Notes, n° 339 (1973). Zbl0271.14017MR49 #299
  15. [15] G. N. TYURINA, Absolute isolatedness of rational singularities and triple rational points, Func. Anal. Appl., 2 (1968), 324-332. Zbl0176.50804

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.