Revista Matemática Iberoamericana


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Volume 19, Issue 2, 2003, pp. 393–412
DOI: 10.4171/RMI/354

Published online: 2003-08-31

Proximity relations for real rank one valuations dominating a local regular ring

Ángel Granja[1] and Cristina Rodríguez[2]

(1) Universidad de León, Spain
(2) Universidad de León, Spain

We study 0-dimensional real rank one valuations centered in a regular local ring of dimension $n\geq 2$ such that the associated valuation ring can be obtained from the regular ring by a sequence of quadratic transforms. We define two classical invariants associated to the valuation (the refined proximity matrix and the multiplicity sequence) and we show that are equivalent data of the valuation.

Keywords: Valuation, real rank, regular ring, quadratic transform

Granja Ángel, Rodríguez Cristina: Proximity relations for real rank one valuations dominating a local regular ring. Rev. Mat. Iberoam. 19 (2003), 393-412. doi: 10.4171/RMI/354