The depth of the associated graded ring of ideals with any reduction number

Details The depth of the associated graded ring of ideals with any reduction number The depth of the associated graded ring of ideals with any reduction number

2002-12-09

arxiv.org/abs/math/0212130v1

Mathematics

Commutative Algebra

13 pages

Scientific paper

Let R be a local Cohen-Macaulay ring, let I be an R-ideal, and let G be the associated graded ring of I. We give an estimate for the depth of G when G is not necessarily Cohen-Macaulay. We assume that I is either equimultiple, or has analytic deviation one, but we do not have any restriction on the reduction number. We also give a general estimate for the depth of G involving the first r+l powers of I, where r denotes the Castelnuovo regularity of G and l denotes the analytic spread of I.

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