Limit trees and generic discriminants of minimal surface singularities

Eric Akéké[1]

  • [1] Centre de Mathématiques et d’Informatique, 39, rue F. Joliot Curie 13453 Marseille cedex 13 (France)

Annales de la faculté des sciences de Toulouse Mathématiques (2008)

  • Volume: 17, Issue: 1, page 37-51
  • ISSN: 0240-2963

Abstract

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According to R. Bondil the dual graph of the minimal resolution of a minimal normal surface singularity determines the generic discriminant of that singularity. In this article we give with combinatorial arguments the link between the limit trees and the generic discriminants of minimal normal surface singularities. The weighted limit trees of a minimal surface singularity determine the generic discriminant of that singularity.

How to cite

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Akéké, Eric. "Limit trees and generic discriminants of minimal surface singularities." Annales de la faculté des sciences de Toulouse Mathématiques 17.1 (2008): 37-51. <http://eudml.org/doc/10080>.

@article{Akéké2008,
abstract = {According to R. Bondil the dual graph of the minimal resolution of a minimal normal surface singularity determines the generic discriminant of that singularity. In this article we give with combinatorial arguments the link between the limit trees and the generic discriminants of minimal normal surface singularities. The weighted limit trees of a minimal surface singularity determine the generic discriminant of that singularity.},
affiliation = {Centre de Mathématiques et d’Informatique, 39, rue F. Joliot Curie 13453 Marseille cedex 13 (France)},
author = {Akéké, Eric},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {minimal singularity; generic discriminant; limit tree},
language = {eng},
month = {6},
number = {1},
pages = {37-51},
publisher = {Université Paul Sabatier, Toulouse},
title = {Limit trees and generic discriminants of minimal surface singularities},
url = {http://eudml.org/doc/10080},
volume = {17},
year = {2008},
}

TY - JOUR
AU - Akéké, Eric
TI - Limit trees and generic discriminants of minimal surface singularities
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2008/6//
PB - Université Paul Sabatier, Toulouse
VL - 17
IS - 1
SP - 37
EP - 51
AB - According to R. Bondil the dual graph of the minimal resolution of a minimal normal surface singularity determines the generic discriminant of that singularity. In this article we give with combinatorial arguments the link between the limit trees and the generic discriminants of minimal normal surface singularities. The weighted limit trees of a minimal surface singularity determine the generic discriminant of that singularity.
LA - eng
KW - minimal singularity; generic discriminant; limit tree
UR - http://eudml.org/doc/10080
ER -

References

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  9. Lê (D.T.) and Tosun (M.).— Combinatorics of rational surface singularities, Comment. Math. Helvetici, 79 (2004). Zbl1060.32016MR2081727
  10. Spivakovsky (M.).— Sandwiched singularities and desingularisation of surfaces by normalized Nash transformations, Ann. Math., 131, p. 411-491 (1990). Zbl0719.14005MR1053487
  11. Teissier (N.).— Variétés polaires II, Multiplicités polaires, Sections planes et conditions de Whitney, Algebraic Geometry, 961, Lecture notes in math., p. 314-491, La Rabida 1981, Springer-Verlag (1982). Zbl0585.14008MR708342
  12. Zariski (O.).— Studies in equisingularity I, equivalent singularities of plane algebroid curves, Amer. J. Math., 87, p. 507-536 (1965). Zbl0132.41601MR177985
  13. Zariski (O.).— General theory of saturation and of satured local rings, Amer. J. Math., 93 (1971). Zbl0226.13013

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