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

Tomás Sánchez Giralda , José J. Aparicio, Ángel Granja Barón

• 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.