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

Aparicio, 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 -