Year: 2026
Type: preprint
Abstract: For an $(n\times N)$-matrix $A$ of rank $n$ with integer entries, Gelfand, Kapranov and Zelevinsky introduce a system of differential equations, called the $A$-hypergeometric system. We define the stable GKZ hypergeometric $\mathcal D$-module using cohomological functors, which is closely related to the $A$-hypergeometric $\mathcal D$-module and the $\mathcal D$-module underlying the better behaved GKZ system introduced by Borisov and Horja. We prove the stable GKZ hypergeometric $\mathcal D$-module is holonomic and is an integrable connection of rank $n!\mathrm{vol}(Δ_\infty)$ on the Zariski open subset parametrizing nondegenerate Laurent polynomials, where $Δ_\infty$ is the Newton polytope at $\infty$.
Source: arXiv (Cornell University)
Author: Fu, Lei
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7130716605
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