Toric ideals which are determinantal

Abstract

Given any equigenerated monomial ideal $I$ with the property that the defining ideal $J$ of the fiber cone $F(I)$ of $I$ is generated by quadratic binomials, we introduce a matrix such that the set of its binomial $2$-minors is a generating set of $J$. In this way, we characterize the fiber cone of sortable and Freiman ideals.