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On the growth of the Betti sequence of the canonical module

Research paper by David A. Jorgensen, Graham J. Leuschke

Indexed on: 10 Jan '07Published on: 10 Jan '07Published in: Mathematische Zeitschrift



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.