Prime and Cohen--Macaulay binomial ideals with linear resolution

Takayuki Hibi; Ayesha Asloob Qureshi; Sara Saeedi Madani

Prime and Cohen--Macaulay binomial ideals with linear resolution

Commutative Algebra 2026-07-24 v1

Authors: Takayuki Hibi , Ayesha Asloob Qureshi , Sara Saeedi Madani

Abstract

Let $I$ be an ideal of a polynomial ring $S$ over a field $K$ for which $I$ is minimally generated by at least two quadratic binomials. Suppose that (i) $I$ is prime, (ii) $S/I$ is Cohen--Macaulay and (iii) $I$ has linear resolution. The question whether $I$ is equal to the ideal of $2$ -minors of a $(2 \times n)$ -matrix of variables is mainly studied.

Cite

@article{arxiv.2607.22127,
  title  = {Prime and Cohen--Macaulay binomial ideals with linear resolution},
  author = {Takayuki Hibi and Ayesha Asloob Qureshi and Sara Saeedi Madani},
  journal= {arXiv preprint arXiv:2607.22127},
  year   = {2026}
}