Gr\"obner bases and final polynomials

Gr\"obner bases and final polynomials

In [4] Sturmfels linked the Hilbert Nullstellensatz to Gr\"obner bases through final polynomials. In (loc. cit.) it was claimed that final polynomials always appear in a lexicographic Gr\"obner basis of a certain ideal. In this paper, we give a counterexample to this claim. We also show ho...

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Bibliographische Detailangaben
Hauptverfasser: Lundgaard, Peter, Poulsen, Andreas Bøgh
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Combinatorics
Mathematics - Commutative Algebra
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Zusammenfassung:In [4] Sturmfels linked the Hilbert Nullstellensatz to Gr\"obner bases through final polynomials. In (loc. cit.) it was claimed that final polynomials always appear in a lexicographic Gr\"obner basis of a certain ideal. In this paper, we give a counterexample to this claim. We also show how the introduction of an extra variable restores the claim in a deformed setup, which we call extended final polynomials.
DOI:10.48550/arxiv.2405.16217