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For a d-dimensional Cohen-Macaulay local ring (R, mn) we study the depth of the associated graded ring of R with respect to an rm-primary ideal I in terms of the Vallabrega-Valla conditions and the length of It+ /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(More)
A central problem in Algebraic Geometry is the classification of several isomorphism classes of objects by considering their deformations and studying the naturally related moduli problems, see [33], [34]. This general strategy has also been applied to singularities. Some classes of singularities with fixed numerical invariants are studied from the moduli(More)
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 Σ . The study of the bigraded Hilbert function of Σ allows us to prove a improved version of Wang’s conjecture and a weak version of Sally’s conjecture, both on the depth of the(More)
Abstract. Let (R,m) be a d-dimensional Cohen-Macaulay local ring. In this note we prove, in a very elementary way, an upper bound of the first normalized Hilbert coefficient of a mprimary ideal I ⊂ R that improves all known upper bounds unless for a finite number of cases, see Remark 1.3. We also provide new upper bounds of the Hilbert functions of I(More)
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