English

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.

Keywords

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

R2 v1 2026-06-21T23:52:07.254Z