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Mathematics > Algebraic Geometry

arXiv:1805.02727 (math)
[Submitted on 7 May 2018 (v1), last revised 1 Feb 2019 (this version, v4)]

Title:Dualizing, projecting, and restricting GKZ systems

Authors: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.
Comments: Made some small fixes based on referee suggestions
Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC)
MSC classes: 14F10 (Primary), 14M25, 32S35, 32C38
Cite as: arXiv:1805.02727 [math.AG]
  (or arXiv:1805.02727v4 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.02727
Related DOI: https://doi.org/10.1016/j.jpaa.2019.03.018

Submission history

From: Avi Steiner [view email]
[v1] Mon, 7 May 2018 20:19:24 UTC (17 KB)
[v2] Sat, 14 Jul 2018 17:49:18 UTC (18 KB)
[v3] Wed, 19 Dec 2018 18:48:52 UTC (19 KB)
[v4] Fri, 1 Feb 2019 00:43:56 UTC (20 KB)
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