Comparing Castelnuovo-Mumford regularity and extended degree: The borderline cases

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12 Scopus citations


Castelnuovo-Mumford regularity and any extended degree function can be thought of as complexity measures for the structure of finitely generated graded modules. A recent result of Doering, Gunston, and Vasconcelos shows that both can be compared in the case of a graded algebra. We extend this result to modules and analyze when the estimate is in fact an equality. A complete classification is obtained if we choose as extended degree the homological or the smallest extended degree. The corresponding algebras are characterized in three ways: by relations among the algebra generators, by using generic initial ideals, and by their Hilbert series.

Original languageEnglish
Pages (from-to)3585-3603
Number of pages19
JournalTransactions of the American Mathematical Society
Issue number9
StatePublished - Sep 2005


  • Castelnuovo-Mumford regularity
  • Extended degree
  • Generic initial ideal
  • Hilbert series
  • Homological degree
  • Smallest extended degree

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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