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Bigraded structures and the depth of blow-up algebras

Published online by Cambridge University Press:  12 July 2007

Gemma Colomé-Nin  and
Juan Elias
Gemma Colomé-Nin
Affiliation:
Departament d'Álgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain (gcolome@ub.edu;
Juan Elias
Affiliation:
Departament d'Álgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spainelias@ub.edu
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Abstract

Let R be a Cohen–Macaulay local ring, and let I ⊂ R be an ideal with minimal reduction J. In this paper we attach to the pair (I, J) a non-standard bigraded module ΣI, J. The study of the bigraded Hilbert function of ΣI, J allows us to prove an improved version of Wang's conjecture and a weak version of Sally's conjecture, both on the depth of the associated graded ring grI(R). The module ΣI, J can be considered as a refinement of the Sally module introduced previously by Vasconcelos.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 6 , December 2006 , pp. 1175 - 1194
Copyright
Copyright © Royal Society of Edinburgh 2006

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