Revista Matemática Iberoamericana

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

Ángel Granja and Cristina Rodríguez

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

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.

Primary Subjects: 13F30
Secondary Subjects: 13H05
Keywords: valuation; real rank; regular ring; quadratic transform

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.rmi/1063050160
Mathematical Reviews number (MathSciNet): MR2023192
Zentralblatt MATH identifier: 02109602

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