Extensions of the multiplicity conjecture

Juan Migliore, Uwe Nagel, Tim R̈omer

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7 Scopus citations


The Multiplicity conjecture of Herzog, Huneke, and Srinivasan states an upper bound for the multiplicity of any graded k-algebra as well as a lower bound for Cohen-Macaulay algebras. In this note we extend this conjecture in several directions. We discuss when these bounds are sharp, find a sharp lower bound in the case of not necessarily arithmetically CohenMacaulay one-dimensional schemes of 3-space, and propose an upper bound for finitely generated graded torsion modules. We establish this bound for torsion modules whose codimension is at most two.

Original languageEnglish
Pages (from-to)2965-2985
Number of pages21
JournalTransactions of the American Mathematical Society
Issue number6
StatePublished - Jun 2008

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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