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


Altinok S.

COMPTES RENDUS MATHEMATIQUE, vol.347, no.11-12, pp.643-646, 2009 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 347 Issue: 11-12
  • Publication Date: 2009
  • Doi Number: 10.1016/j.crma.2009.04.010
  • Title of Journal : COMPTES RENDUS MATHEMATIQUE
  • Page Numbers: pp.643-646

Abstract

There is a correspondence between the set of functions in the maximal ideal of the local ring of a rational surface singularity and the set epsilon(+)(E) consisting of certain effective divisors supported oil the exceptional fiber E of it resolution of the singularity. Given an element Y is an element of epsilon(+)(E) and a non-Tjurina component N of Y, we verify a formula for the least element of the set of divisors X is an element of epsilon(+)(E) greater than or equal to Y + N stated but not proved in Tosun (1999). To cite this article: S. Altillok, C. R. Acad. Sci. Paris, Ser. I 347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.