Robust Toric Ideals
Commutative Algebra
2013-06-20 v2 Algebraic Geometry
Combinatorics
Abstract
We call an ideal in a polynomial ring robust if it can be minimally generated by a universal Gr\"obner basis. In this paper we show that robust toric ideals generated by quadrics are essentially determinantal. We then discuss two possible generalizations to higher degree, providing a tight classification for determinantal ideals, and a counterexample to a natural extension for Lawrence ideals. We close with a discussion of robustness of higher Betti numbers.
Cite
@article{arxiv.1304.0603,
title = {Robust Toric Ideals},
author = {Adam Boocher and Elina Robeva},
journal= {arXiv preprint arXiv:1304.0603},
year = {2013}
}
Comments
Minor corrections and new introduction