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

José J. Aparicio; Angel Granja; Tomás Sánchez-Giralda

Revista Matemática Iberoamericana (1999)

- Volume: 15, Issue: 3, page 621-634
- ISSN: 0213-2230

## Access Full Article

top## Abstract

top## How to cite

topAparicio, José J., Granja, Angel, and Sánchez-Giralda, Tomás. "On proximity relations for valuations dominating a two-dimensional regular local ring.." Revista Matemática Iberoamericana 15.3 (1999): 621-634. <http://eudml.org/doc/39576>.

@article{Aparicio1999,

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)\}j ≥ 0 which is determined by the proximity relations of the successive quadratic transformations at the points determined by a valuation ν. 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.},

author = {Aparicio, José J., Granja, Angel, Sánchez-Giralda, Tomás},

journal = {Revista Matemática Iberoamericana},

keywords = {Dimensiones; Invariantes; Anillo local; quadratic transformations of regular local rings; valuation ring; proximity relation; proximity sequence; curve singularities},

language = {eng},

number = {3},

pages = {621-634},

title = {On proximity relations for valuations dominating a two-dimensional regular local ring.},

url = {http://eudml.org/doc/39576},

volume = {15},

year = {1999},

}

TY - JOUR

AU - Aparicio, José J.

AU - Granja, Angel

AU - Sánchez-Giralda, Tomás

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

JO - Revista Matemática Iberoamericana

PY - 1999

VL - 15

IS - 3

SP - 621

EP - 634

AB - 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)}j ≥ 0 which is determined by the proximity relations of the successive quadratic transformations at the points determined by a valuation ν. 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.

LA - eng

KW - Dimensiones; Invariantes; Anillo local; quadratic transformations of regular local rings; valuation ring; proximity relation; proximity sequence; curve singularities

UR - http://eudml.org/doc/39576

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.