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

Ian Aberbach·Laura Ghezzi·Huy Tai Ha
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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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Ian Aberbach, Laura Ghezzi, Huy Tai Ha. 2002-12-09. The depth of the associated graded ring of ideals with any reduction number. https://arxiv.org/abs/math/0212130

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