On the depth of the tangent cone and the growth of the Hilbert function
Authors:
Juan Elias
Affiliation:
Departament d'Àlgebra i Geometria, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
Abstract:
For a dimensional Cohen-Macaulay local ring we study the depth of the associated graded ring of with respect to an -primary ideal in terms of the Vallabrega-Valla conditions and the length of , where is a minimal reduction of and . As a corollary we generalize Sally's conjecture on the depth of the associated graded ring with respect to a maximal ideal to -primary ideals. We also study the growth of the Hilbert function.