The depth of the associated graded ring of ideals with any reduction number
Commutative Algebra
2007-05-23 v1 Algebraic Geometry
Abstract
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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Cite
@article{arxiv.math/0212130,
title = {The depth of the associated graded ring of ideals with any reduction number},
author = {Ian Aberbach and Laura Ghezzi and Huy Tai Ha},
journal= {arXiv preprint arXiv:math/0212130},
year = {2007}
}
Comments
13 pages