Collectanea Mathematica

, Volume 67, Issue 3, pp 357–362

Linear syzygies, flag complexes, and regularity

  • Alexandru Constantinescu
  • Thomas Kahle
  • Matteo Varbaro

DOI: 10.1007/s13348-015-0141-3

Cite this article as:
Constantinescu, A., Kahle, T. & Varbaro, M. Collect. Math. (2016) 67: 357. doi:10.1007/s13348-015-0141-3


We show that for every \(r\in \mathbb {Z}_{>0}\) there exist monomial ideals generated in degree two, with linear syzygies, and regularity of the quotient equal to \(r\). For Gorenstein ideals we prove that the regularity of their quotients can not exceed four, thus showing that for \(d > 4\) every triangulation of a \(d\)-manifold has a hollow square or simplex. We also show that for most monomial ideals generated in degree two and with linear syzygies the regularity is \(O(\log (\log (n))\), where \(n\) is the number of variables.

Mathematics Subject Classification

Primary 13F55 Secondary 13D02 20F55 

Copyright information

© Universitat de Barcelona 2015

Authors and Affiliations

  • Alexandru Constantinescu
    • 1
  • Thomas Kahle
    • 2
  • Matteo Varbaro
    • 3
  1. 1.Mathematisches InstitutFreie Universität BerlinBerlinGermany
  2. 2.Fakultät für MathematikOvGU MagdeburgMagdeburgGermany
  3. 3.Dipartimento di MatematicaUniversità di GenovaGenoaItaly

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