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

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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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Reproducció digital del document publicat en format paper, proporcionada per JSTOR http://www.jstor.org/stable/118037

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Transactions of the American Mathematical Society, 1999, vol. 351, núm. 10, p. 4027-4042.

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
On the depth of the tangent cone and the growth of the Hilbert function