Toric ideals generated by circuits
Commutative Algebra
2012-07-27 v3 Combinatorics
Abstract
Let I be the toric ideal of a homogeneous normal configuration. We prove that I is generated by circuits if and only if each unbalanced circuit of I has a "connector" which is a linear combination of circuits with a square-free term. In particular if each circuit of I with non-square-free terms is balanced, then I is generated by circuits. As a consequence we prove that the toric ideal of a normal edge subring of a multigraph is generated by circuits with a square-free term.
Cite
@article{arxiv.0812.0195,
title = {Toric ideals generated by circuits},
author = {Jose Martinez-Bernal and Rafael H. Villarreal},
journal= {arXiv preprint arXiv:0812.0195},
year = {2012}
}
Comments
Apostolos Thoma has pointed out to us that the condition of Theorem 3.2 is not sufficient for the normality of the edge subring. Algebra Colloquium, to appear