JournalsrmiVol. 15, No. 3pp. 621–634

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

  • José Juan Aparicio

    Universidad de Valladolid, Spain
  • Ángel Granja

    Universidad de León, Spain
  • Tomás Sánchez-Giralda

    Universidad de Valladolid, Spain
On proximity relations for valuations dominating a two-dimensional regular local ring cover
Download PDF

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 δν={δν(j)}j0\delta_\nu = \lbrace \delta_\nu (j)\rbrace_{j≥0} which is determined by the proximity relations of the successive quadratic transformations at the points determined by a valuation ν\nu. 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.

Cite this article

José Juan Aparicio, Ángel Granja, Tomás Sánchez-Giralda, On proximity relations for valuations dominating a two-dimensional regular local ring. Rev. Mat. Iberoam. 15 (1999), no. 3, pp. 621–634

DOI 10.4171/RMI/267