The exceptional-arrangement characterization for dual GKZ systems

Let $A$ be an integer matrix, let $S_A$ be its semigroup ring, and let $\mathfrak m$ be its homogeneous maximal ideal. For each $i<\dim(S_A)$, let $H^i_{\mathfrak m}(S_A)$ denote the corresponding local cohomology module, and let the $A$-exceptional arrangement be the union of the quasi-degrees of these modules. Exceptional-arrangement conjecture. The set of parameters $\beta$ for which the dual of $H_A(\beta)$ is a classical GKZ-system agrees with the complement of the $A$-exceptional arrangement. The paper proves the corresponding statement for generic parameters, while the asserted exact description of all parameters remains open in the supplied text.