The covering conjecture for Aomoto–Gel'fand hypergeometric systems

Let $E(n,m)$ be the Aomoto–Gel'fand hypergeometric system on the Grassmannian $G(n,m)$, and let $GKZ$ denote suitable Gelfand–Kapranov–Zelevinsky hypergeometric systems. The parameter space of $E(n,m)$ is covered by Zariski-open subsets of toric varieties.

Covering conjecture. On each member of this open covering, the system $E(n,m)$ is represented locally by a $GKZ$ system; equivalently, the hypergeometric $\mathcal{D}$-modules of $E(n,m)$ have coverings by $\mathcal{D}$-modules of suitable $GKZ$ systems.

This is proposed as a generalization of the authors' explicit constructions for the case of $E(3,6)$. The statement concerns the relationship between Aomoto–Gel'fand systems on Grassmannians and toric GKZ systems; no resolution of the general claim is given in the source.