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arXiv · 1805.02727

Dualizing, projecting, and restricting GKZ systems

Avi Steiner
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Abstract

Let $A$ be an integer matrix, and assume that its semigroup ring $\mathbb{C}[\mathbb{N}A]$ is normal. Fix a face $F$ of the cone of $A$. We show that the projection and restriction of an $A$-hypergeometric system to the coordinate subspace corresponding to $F$ are essentially $F$-hypergeometric; moreover, at most one of them is nonzero. We also show that, if $A$ is in addition homogeneous, the holonomic dual of an $A$-hypergeometric system is itself $A$-hypergeometric. This extends a result of Uli Walther, proving a conjecture of Nobuki Takayama in the normal homogeneous case.

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Avi Steiner. 2018-05-07. Dualizing, projecting, and restricting GKZ systems. https://doi.org/10.1016/j.jpaa.2019.03.018

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