Toric ideals which are determinantal

Document Type : Research Paper

Authors

1 Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran

2 Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan,Iran

Abstract

Consider the polynomial ring $S=\mathbb{K}[x_1,\ldots, x_n]$ 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 $2$-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

References

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