Proximity relations for real rank one valuations dominating a local regular ring. (English) Zbl 1094.13535

Summary: 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.


13F30 Valuation rings
13H05 Regular local rings
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