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

2002/12/09 by Ian Aberbach, Aberbach, Ian, Laura Ghezzi +3
Mathematics · #13A30 #13C15 #14J26 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13A30 #msc:13C15 #msc:14J26

paper · pdf · doi:10.48550/arxiv.math/0212130

13 pages

arxiv created 2002/12/09 · arxiv updated 2009/11/30

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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