On the growth of the Betti sequence of the canonical module
Commutative Algebra
2007-05-23 v2
Abstract
We study the growth of the Betti sequence of the canonical module of a Cohen-Macaulay local ring. It is an open question whether this sequence grows exponentially whenever the ring is not Gorenstein. We answer the question of exponential growth affirmatively for a large class of rings, and prove that the growth is in general not extremal. As an application of growth, we give criteria for a Cohen-Macaulay ring possessing a canonical module to be Gorenstein.
Cite
@article{arxiv.math/0603693,
title = {On the growth of the Betti sequence of the canonical module},
author = {David A. Jorgensen and Graham J. Leuschke},
journal= {arXiv preprint arXiv:math/0603693},
year = {2007}
}
Comments
12 pages. version 2: includes omitted author contact information