Hilbert Stratification and Parametric Gröbner Bases

  • Laureano Gonzalez–Vega
  • Carlo Traverso
  • Alberto Zanoni
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3718)


In this paper we generalize a method to analyze inhomogeneous polynomial systems containing parameters. In particular, the Hilbert function is used as a tool to check that the specialization of a “generic” Gröbner basis of the parametric polynomial system (computed in a polynomial ring having both parameters and unknowns as variables) is a Gröbner basis of the specialized system. Extending the analysis, we can also build the so-called Hilbert stratification of the associated variety. We classify the possible specializations according to the value of the Hilbert function of the specialized system. Some computation examples with the PoSSoLib are reported.

Keywords and phrases

Gröbner bases Hilbert function Specialization 

AMS Subject Classification

68W30 13P10 13F20 13D40 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Laureano Gonzalez–Vega
    • 1
  • Carlo Traverso
    • 2
  • Alberto Zanoni
    • 2
  1. 1.Dpto. Matemáticas, Estadística y Computación, Facultad de ScienciasUniversidad de CantabriaSantanderSpain
  2. 2.Dipartimento di Matematica “Leonida Tonelli”Università di PisaPisaItaly

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