Gr\"obner bases of simplicial toric ideals
M. Hellus, J. Stueckrad, L. T. Hoa
TL;DR
This paper provides bounds on the maximal degree of specific Gr"obner bases for simplicial toric ideals, approaching the bounds suggested by Eisenbud-Goto's Conjecture on Castelnuovo-Mumford regularity.
Contribution
It introduces new bounds for the degrees of Gr"obner bases in the context of simplicial toric ideals, aligning closely with a major conjecture in algebraic geometry.
Findings
Bounds are close to Eisenbud-Goto's conjecture
Provides theoretical limits for Gr"obner basis degrees
Enhances understanding of toric ideal algebraic properties
Abstract
Bounds for the maximal degree of certain Gr\"obner bases of simplicial toric ideals are given. These bounds are close to the bound stated in Eisenbud-Goto's Conjecture on the Castelnuovo-Mumford regularity.
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