Toric ideals which are determinantal

Consider the polynomial ring S=\mathbb{K}[x_۱,\ldots, x_n] over a field \mathbb{K}. For any equigenerated monomial ideal I \subset S with the defining ideal J of the fiber cone \F(I) generated by quadratic binomials, we introduce a matrix. The key observation is that the set of binomial ۲-minors of this matrix serves as a generating set for J. This framework in particular provides a characterization of the fiber cone for Freiman ideals, as well as offering a specific characterization for the fiber cone of sortable ideals.

Keywords:

fiber cone , toric ideal , sortable ideal , Freiman ideal