Revista Matemática Iberoamericana

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

Ángel Granja and Cristina Rodríguez

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Abstract

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.

Article information

Source
Rev. Mat. Iberoamericana, Volume 19, Number 2 (2003), 393-412.

Dates
First available in Project Euclid: 8 September 2003

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1063050160

Mathematical Reviews number (MathSciNet)
MR2023192

Zentralblatt MATH identifier
1094.13535

Subjects
Primary: 13F30: Valuation rings [See also 13A18]
Secondary: 13H05: Regular local rings

Keywords
valuation real rank regular ring quadratic transform

Citation

Granja, Ángel; Rodríguez, Cristina. Proximity relations for real rank one valuations dominating a local regular ring. Rev. Mat. Iberoamericana 19 (2003), no. 2, 393--412. https://projecteuclid.org/euclid.rmi/1063050160


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