On the growth of the Betti sequence of the canonical module

2006/03/29 by David A. Jorgensen, Jorgensen, David A., Graham Leuschke +1 · 1 citation
Mathematics · #13C14 #13D02 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.math/0603693

openalex publication_date 2006/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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