Dualizing, projecting, and restricting GKZ systems

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.

arXiv commentMade some small fixes based on referee suggestions

References in corpus (6)

• Equivariant D-modules
• Hypergeometric D-modules and twisted Gauss-Manin systems
• Laurent Polynomials, GKZ-hypergeometric Systems and Mixed Hodge Modules
• Isomorphism classes of A-hypergeometric systems
• $A$-Hypergeometric Modules and Gauss--Manin Systems
• Gauss-Manin systems of families of Laurent polynomials and A-hypergeometric systems

Cited by in corpus (1)

• Algebraic aspects of hypergeometric differential equations