The GKZ hypergeometric $\mathcal D$-module
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915873463205888 |
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| author | Fu, Lei |
| author_facet | Fu, Lei |
| contents | 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 $\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16941 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The GKZ hypergeometric $\mathcal D$-module Fu, Lei Algebraic Geometry Primary 14F10. Secondary 33C70 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 $\infty$. |
| title | The GKZ hypergeometric $\mathcal D$-module |
| topic | Algebraic Geometry Primary 14F10. Secondary 33C70 |
| url | https://arxiv.org/abs/2602.16941 |