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1999

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/7766

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

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Abstract

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

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Anells locals, Ideals (Àlgebra), Homologia, Funcions característiques, Geometria algebraica

Subject (English)

Associated graded rings of ideals, Homological methods, Hilbert-Samuel and Hilbert-Kunz functions, Poincaré series, Local rings and semilocal rings

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ELÍAS GARCÍA, Joan. On the depth of the tangent cone and the growth of the Hilbert function. Transactions of the American Mathematical Society. 1999. Vol. 351, num. 10, pags. 4027-4042. ISSN 1088-6850. [consulted: 18 of June of 2026]. Available at: https://hdl.handle.net/2445/7766

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