Quasi-stability versus Genericity

  • Amir Hashemi
  • Michael Schweinfurter
  • Werner M. Seiler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7442)


Quasi-stable ideals appear as leading ideals in the theory of Pommaret bases. We show that quasi-stable leading ideals share many of the properties of the generic initial ideal. In contrast to genericity, quasi-stability is a characteristic independent property that can be effectively verified. We also relate Pommaret bases to some invariants associated with local cohomology, exhibit the existence of linear quotients in Pommaret bases and prove some results on componentwise linear ideals.


Betti Number Polynomial Ideal Monomial Ideal Free Resolution Minimal Basis 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Amir Hashemi
    • 1
  • Michael Schweinfurter
    • Werner M. Seiler
      1. 1.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran

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