On the growth of the Betti sequence of the canonical module

David A. Jorgensen, Graham J. Leuschke

Research output: Contribution to journalArticle

9 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)647-659
Number of pages13
JournalMathematische Zeitschrift
Volume256
Issue number3
DOIs
StatePublished - Jul 2007

ASJC Scopus subject areas

  • Mathematics(all)

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