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.
Jorgensen, David A. and Leuschke, Graham J., "On the Growth of the Betti Sequence of the Canonical Module" (2006). Mathematics Faculty Scholarship. Paper 35.
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