Document Type
Article
Date
4-3-2006
Disciplines
Mathematics
Description/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.
Recommended Citation
Jorgensen, David A. and Leuschke, Graham J., "On the Growth of the Betti Sequence of the Canonical Module" (2006). Mathematics - All Scholarship. 35.
https://surface.syr.edu/mat/35
Source
Harvested from arXiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
This manuscript is from arXiv.org, more information see http://arxiv.org/abs/math/0603693