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

Autores: Tomás Sánchez Giralda , José J. Aparicio, Ángel Granja Barón
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 15, Nº 3, 1999, págs. 621-634
Idioma: inglés
DOI: 10.4171/rmi/267
Títulos paralelos:
- Relaciones de proximidad para valoraciones que dominan un anillo regular local de dos dimensiones.
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Resumen
- 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.