Rings that are homologically of minimal multiplicity
arXiv:0904.3982
Abstract
Let R be a local Cohen-Macaulay ring with canonical module ω_R. We investigate the following question of Huneke: If the sequence of Betti numbers \{β_i^R(ω_R)\} has polynomial growth, must R be Gorenstein? This question is well-understood when R has minimal multiplicity. We investigate this question for a more general class of rings which we say are homologically of minimal multiplicity. We provide several characterizations of the rings in this class and establish a general ascent and descent result.
arXiv comment23 pages, minor revisions for v.2, final version, to appear in Comm. Algebra