There is a correspondence between the set of functions in the maximal ideal of the local ring of a rational surface singularity ξ and the set consisting of certain effective divisors supported on the exceptional fiber E of a resolution of the singularity. Given an element and a non-Tjurina component N of Y, we verify a formula for the least element of the set of divisors greater than or equal to stated but not proved in Tosun (1999).
Il existe une correspondance entre l'ensemble des fonctions de l'idéal maximal de l'anneau local en une singularité rationnelle ξ d'une surface et un ensemble de diviseurs effectifs portés par la fibre exceptionnelle E d'une résolution de cette singularité. Étant donné un élément et une composante N de Y qui n'est pas Tjurina, nous établissons une formule donnant le plus petit élément de l'ensemble des diviseurs supérieur ou égal à , indiquée mais non démontrée dans Tosun (1999).
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@article{CRMATH_2009__347_11-12_643_0,
author = {Alt{\i}nok, Selma},
title = {On an analog of {Pinkham's} theorem for {non-Tjurina} components of rational singularities},
journal = {Comptes Rendus. Math\'ematique},
pages = {643--646},
publisher = {Elsevier},
volume = {347},
number = {11-12},
year = {2009},
doi = {10.1016/j.crma.2009.04.010},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.04.010/}
}
TY - JOUR AU - Altınok, Selma TI - On an analog of Pinkham's theorem for non-Tjurina components of rational singularities JO - Comptes Rendus. Mathématique PY - 2009 SP - 643 EP - 646 VL - 347 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.04.010/ DO - 10.1016/j.crma.2009.04.010 LA - en ID - CRMATH_2009__347_11-12_643_0 ER -
%0 Journal Article %A Altınok, Selma %T On an analog of Pinkham's theorem for non-Tjurina components of rational singularities %J Comptes Rendus. Mathématique %D 2009 %P 643-646 %V 347 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.04.010/ %R 10.1016/j.crma.2009.04.010 %G en %F CRMATH_2009__347_11-12_643_0
Altınok, Selma. On an analog of Pinkham's theorem for non-Tjurina components of rational singularities. Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 643-646. doi : 10.1016/j.crma.2009.04.010. http://www.numdam.org/articles/10.1016/j.crma.2009.04.010/
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