On proximity relations for valuations dominating a two-dimensional regular local ring

  1. Sánchez Giralda, Tomás
  2. Aparicio, José J.
  3. Granja Barón, Ángel
Revista matemática iberoamericana

ISSN: 0213-2230

Year of publication: 1999

Volume: 15

Issue: 3

Pages: 621-634

Type: Article

DOI: 10.4171/RMI/267 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Revista matemática iberoamericana


Abstract. The purpose of this paper is to define a new numerical invariant of valuations centered in-a regular two-dimensional regular local ring. For this, we define a sequence of non-negative rational numbers delta v = [delta v,(j)] sub j>-0 which is determined by the proximity relations of the successive quadratic transformations at the points determined by a valuation v. This sequence is characterized by seven combinatorial properties, so that any sequence of non-negative rational numbers having the above properties is the sequence associated to a valuation.