Work

Koszul binomial edge ideals

Year: 2026

Type: article

Abstract: The study of Koszul binomial edge ideals was initiated by V. Ene, J. Herzog, and T. Hibi in 2014, who found necessary conditions for Koszulness. The binomial edge ideal $J_G$ associated to a finite simple graph G is always generated by quadrics. It has a quadratic Gröbner basis if and only if the graph G is closed. However, there are many known nonclosed graphs G where $J_G$ is Koszul. We characterize the Koszul binomial edge ideals by a simple combinatorial property of the graph G .

Source: Forum of Mathematics Sigma

DOI: 10.1017/fms.2025.10153

Authors: Adam LaClair, Matthew Mastroeni, Jason McCullough, Irena Peeva

Institutions: University of Nebraska–Lincoln, SUNY Polytechnic Institute, Iowa State University, Cornell University

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,650

Funders: National Science Foundation, Simons Foundation