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On adjacent complete ideals above a given complete ideal

Published online by Cambridge University Press:  30 March 2010

Maria Alberich-Carramiñana  and
Jesús Fernández-Sánchez
Maria Alberich-Carramiñana
Affiliation:
Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Av. Diagonal 647, 08028 Barcelona, Spain ([email protected]) and Institut de Robòtica i Informàtica Industrial (CSIC-UPC), Llorens i Artigues 4–6, 08028 Barcelona, Spain
Jesús Fernández-Sánchez
Affiliation:
Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Av. Diagonal 647, 08028 Barcelona, Spain ([email protected])
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Abstract

Given a complete m-primary ideal J in a local regular two-dimensional ring (R,m), we describe every adjacent complete ideal above J as the integral closure of some ideal (f, g) for suitable f, g associated to J. We also provide a geometrical procedure that gives its base points, thus determining its equisingularity class. We decompose the set IJ of these adjacent ideals in terms of the Rees valuations of J. As a consequence, we obtain a geometrical characterization of the finiteness of IJ.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 2 , April 2010 , pp. 225 - 239
Copyright
Copyright © Royal Society of Edinburgh 2010

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