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

Abstract

We study 0-dimensional real rank one valuations centered in a regular local ring of dimension $n\ge 2$ 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.