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Transactions of the American Mathematical Society

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On the depth of the tangent cone
and the growth of the Hilbert function


Author: Juan Elias
Journal: Trans. Amer. Math. Soc. 351 (1999), 4027-4042
MSC (1991): Primary 13A30, 13D40, 13H10
DOI: https://doi.org/10.1090/S0002-9947-99-02278-3
Published electronically: April 20, 1999
MathSciNet review: 1491860
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Abstract | References | Similar Articles | Additional Information

Abstract: For a $d-$dimensional Cohen-Macaulay local ring $(R, \mathbf{m})$ we study the depth of the associated graded ring of $R$ with respect to an $ \textbf{ m}$-primary ideal $I$ in terms of the Vallabrega-Valla conditions and the length of $I^{t+1}/JI^{t}$, where $J$ is a $J$ minimal reduction of $I$ and $t\ge 1$. As a corollary we generalize Sally's conjecture on the depth of the associated graded ring with respect to a maximal ideal to $\mathbf{m}$-primary ideals. We also study the growth of the Hilbert function.


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Additional Information

Juan Elias
Affiliation: Departament d’Àlgebra i Geometria, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
Email: elias@cerber.mat.ub.es

DOI: https://doi.org/10.1090/S0002-9947-99-02278-3
Received by editor(s): June 24, 1997
Published electronically: April 20, 1999
Additional Notes: Partially supported by DGICYT PB94-0850
Article copyright: © Copyright 1999 American Mathematical Society

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