Gr\"obner bases of simplicial toric ideals
M. Hellus, J. Stueckrad, L. T. Hoa
TL;DR
This paper provides bounds on the maximum degree of minimal Gr"obner bases for simplicial toric ideals, relating closely to the Eisenbud-Goto conjecture on regularity, advancing understanding in algebraic geometry.
Contribution
It introduces new bounds for the degrees of Gr"obner bases of simplicial toric ideals, connecting these bounds to a major conjecture in algebraic geometry.
Findings
Bounds are close to Eisenbud-Goto's conjecture on regularity
Provides theoretical limits for degrees of Gr"obner bases
Enhances understanding of simplicial toric ideals
Abstract
Bounds for the maximum degree of a minimal Gr\"obner basis of simplicial toric ideals with respect to the reverse lexicographic order are given. These bounds are close to the bound stated in Eisenbud-Goto's Conjecture on the Castelnuovo-Mumford regularity.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic Geometry and Number Theory