Strongly robust toric ideals in codimension 2

TL;DR

This paper characterizes strongly robust toric ideals in codimension 2 by their Gale diagrams, providing a complete classification and answering a specific open question in the field.

Contribution

It offers a complete characterization of codimension 2 strongly robust toric ideals using Gale diagrams, advancing understanding of their algebraic structure.

Findings

Characterization of codimension 2 strongly robust toric ideals

Gale diagrams as a classification tool

Positive resolution of an open question in the field

Abstract

A homogeneous ideal is robust if its universal Gr\"obner basis is also a minimal generating set. For toric ideals, one has the stronger definition: A toric ideal is strongly robust if its Graver basis equals the set of indispensable binomials. We characterize the codimension 2 strongly robust toric ideals by their Gale diagrams. This gives a positive answer to a question of Petrovic, Thoma, and Vladoiu in the case of codimension 2 toric ideals.