An improved multiplicity conjecture for codimension 3 Gorenstein algebras

Juan C. Migliore, Uwe Nagel, Fabrizio Zanello

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


The Multiplicity Conjecture is a deep problem relating the multiplicity (or degree) of a Cohen-Macaulay standard graded algebra with certain extremal graded Betti numbers in its minimal free resolution. In the case of level algebras of codimension three, Zanello has proposed a stronger conjecture. We prove this conjecture in the Gorenstein case.

Original languageEnglish
Pages (from-to)112-119
Number of pages8
JournalCommunications in Algebra
Issue number1
StatePublished - Jan 2008

Bibliographical note

Funding Information:
The research contained in this article was performed during the third author’s visit to the first author at the University of Notre Dame, and that visit was supported by a grant of the Vetenskåpsradet (Swedish Research Council) and a grant of the Department of Mathematics of the University of Notre Dame. Moreover, the third author was funded by the Göran Gustafsson Foundation.

Copyright 2008 Elsevier B.V., All rights reserved.


  • Betti numbers
  • Gorenstein algebras
  • Hilbert functions
  • Level algebras
  • Minimal free resolution
  • Multiplicity conjecture

ASJC Scopus subject areas

  • Algebra and Number Theory


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