English

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.

Keywords

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