A-hypergeometric modules and Gauss-Manin systems

JOURNAL OF ALGEBRA

卷:524

Article

Steiner, Avi¹ 

[1] Purdue Univ, Dept Math, 150 N Univ St, W Lafayette, IN 47907 USA

关键词: Algebraic geometry;    Commutative algebra;    D-modules;    Local cohomology;    Affine semigroup rings;    Toric varieties;    GKZ systems;   

DOI  :  10.1016/j.jalgebra.2019.01.008

来源: Elsevier

【 摘 要 】

Let A be a d x n integer matrix. Gel'fand et al. proved that most A-hypergeometric systems have an interpretation as a Fourier-Laplace transform of a direct image. The set of parameters for which this happens was later identified by Schulze and Walther as the set of not strongly resonant parameters of A. A similar statement relating A-hypergeometric systems to exceptional direct images was proved by Reichelt. In this article, we consider a hybrid approach involving neighborhoods U of the torus of A and consider compositions of direct and exceptional direct images. Our main results characterize for which parameters the associated A-hypergeometric system is the inverse Fourier-Laplace transform of such a mixed Gauss-Manin system. In order to describe which U work for such a parameter, we introduce the notions of fiber support and cofiber support of a D-module. If the semigroup ring C[NA] is normal, we show that every A-hypergeometric system is mixed Gauss-Manin. We also give an explicit description of the neighborhoods U which work for each parameter in terms of primitive integral support functions. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free