On the growth of the Betti sequence of the canonical module

Details On the growth of the Betti sequence of the canonical module On the growth of the Betti sequence of the canonical module

2006-03-29

arxiv.org/abs/math/0603693v2

Mathematics

Commutative Algebra

12 pages. version 2: includes omitted author contact information

Scientific paper

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.

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