A multiplicity bound for graded rings and a criterion for the Cohen-Macaulay property

2014/01/23 by Huneke, Craig, Mantero, Paolo, McCullough, Jason +1
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1401.6216

Abstract

Let R be a polynomial ring over a field. We prove an upper bound for the multiplicity of R/I when I is a homogeneous ideal of the form I=J+(F), where J is a Cohen-Macaulay ideal and F∉ J. The bound is given in terms of two invariants of R/J and the degree of F. We show that ideals achieving this upper bound have high depth, and provide a purely numerical criterion for the Cohen-Macaulay property. Applications to quasi-Gorenstein rings and almost complete intersections are given.

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