Hypergeometric D-modules and twisted Gauss-Manin systems

JOURNAL OF ALGEBRA

卷:322

Article

Schulze, Mathias¹  Walther, Uli² 

[1] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

关键词: Toric ring;    Hypergeometric system;    Euler-Koszul homology;    D-module;    Direct image;    Gauss-Manin system;   

DOI  :  10.1016/j.jalgebra.2008.09.010

来源: Elsevier

【 摘 要 】

The Euler-Koszul complex is the fundamental tool in the homological study of A-hypergeometric differential systems and functions. We compare Euler-Koszul homology with D-module direct images from the torus to the base space through orbits in the corresponding toric variety. Our approach generalizes a result by Gel'fand et al. [I.M. Gel'fand, M.M. Kapranov, A.V. Zelevinsky, Generalized Euler integrals and A-hypergeometric functions, Adv. Math. 84 (2) (1990) 255-271, MR MR1080980 (92e:33015), Thm. 4.6] and yields a simpler, more algebraic proof. In the process we extend the Euler-Koszul functor to a category of infinite toric modules and describe multigraded localizations of Euler-Koszul homology. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free