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arXiv · 2405.16217

Gr\"obner bases and final polynomials

Peter Lundgaard·Andreas Bøgh Poulsen
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Abstract

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.

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Peter Lundgaard, Andreas Bøgh Poulsen. 2024-05-25. Gr\"obner bases and final polynomials. https://arxiv.org/abs/2405.16217

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