Regularity bounds for Koszul cycles

Aldo Conca*, Satoshi Murai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We study the Castelnuovo-Mumford regularity of the module of Koszul cycles Zt(I,M) of a homogeneous ideal I in a polynomial ring S with respect to a graded module M in the homological position t ∈ N. Under mild assumptions on the base field we prove that reg Zt(I,S) is a subadditive function of t when dim S/I = 0. For Borel-fixed ideals I, J we prove that reg Zt(I,S/J) ≤ t(1 + reg I) + regS/J, a result already announced by Bruns, Conca and Römer.

Original languageEnglish
Pages (from-to)493-503
Number of pages11
JournalProceedings of the American Mathematical Society
Issue number2
Publication statusPublished - 2015
Externally publishedYes


  • Castelnuovo-Mumford regularity
  • Koszul cycles
  • Koszul homology

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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