On an analog of Pinkham's theorem for non-Tjurina components of rational singularities

Altınok, Selma

doi:10.1016/j.crma.2009.04.010

Analytic Geometry

On an analog of Pinkham's theorem for non-Tjurina components of rational singularities
[Sur un analogue du théorème de Pinkham pour les composantes des singularités rationnelles qui ne sont pas Tjurina]

Présenté par : Bernard Malgrange

Altınok, Selma ¹

¹ Adnan Menderes Üniversitesi, Matematik Bölümü, 09100 Aydın, Turkey

Comptes Rendus. Mathématique, Tome 347 (2009) no. 11-12, pp. 643-646.

Résumé
Abstract

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 $E^{+} (E)$ de diviseurs effectifs portés par la fibre exceptionnelle E d'une résolution de cette singularité. Étant donné un élément $Y \in E^{+} (E)$ 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 $X \in E^{+} (E)$ supérieur ou égal à $Y + N$ , indiquée mais non démontrée dans Tosun (1999).

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 $E^{+} (E)$ consisting of certain effective divisors supported on the exceptional fiber E of a resolution of the singularity. Given an element $Y \in E^{+} (E)$ and a non-Tjurina component N of Y, we verify a formula for the least element of the set of divisors $X \in E^{+} (E)$ greater than or equal to $Y + N$ stated but not proved in Tosun (1999).

Reçu le : 2008-03-06
Accepté le : 2009-04-02
Publié le : 2009-04-24

DOI : 10.1016/j.crma.2009.04.010

Affiliations des auteurs :

Altınok, Selma ¹

¹ Adnan Menderes Üniversitesi, Matematik Bölümü, 09100 Aydın, Turkey

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Altınok, Selma. On an analog of Pinkham's theorem for non-Tjurina components of rational singularities. Comptes Rendus. Mathématique, Tome 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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