Gr\"obner bases and final polynomials
Commutative Algebra
2024-05-28 v1 Combinatorics
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.
Cite
@article{arxiv.2405.16217,
title = {Gr\"obner bases and final polynomials},
author = {Peter Lundgaard and Andreas Bøgh Poulsen},
journal= {arXiv preprint arXiv:2405.16217},
year = {2024}
}
Comments
3 pages