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Gröbner bases and final polynomials

2024/05/25 by Peter Lundgaard, Lundgaard, Peter, Andreas Bøgh Poulsen +1
Mathematics · #13P10 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2405.16217

openalex publication_date 2024/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In [4] Sturmfels linked the Hilbert Nullstellensatz to Gröbner bases through final polynomials. In (loc. cit.) it was claimed that final polynomials always appear in a lexicographic Gröbner 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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