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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 I t+1 /JI t , 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)
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 I,J. The study of the bigraded Hilbert function of Σ I,J 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 associated(More)
This is a list of corrections for those typos in the paper that I am aware of. Information on new discoveries sent to avramov@math.purdue.edu will be most helpful. page line reads should read 16 5 3 (a b) = ?a ^ @ 1 (b) + @ 1 (a)b 3 (a b) = ?a ^ @ 2 (b) + @ 1 (a)b 38 {16 for n 1 for n 0 41 4 Example 15.2.8 Example 5.2.8 42 1 If a bounded Is a bounded 47 9(More)
CONTENTS Introduction 1 1. Truncations of curve singularities. 3 2. Families of embedded curve singularities. 8 3. Moduli space of curve singularities. 12 4. Local properties of the moduli space. 26 References 31 INTRODUCTION A central problem in Algebraic Geometry is the classification of several isomorphism classes of objects by considering their(More)
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