Hypergeometric D-modules and twisted Gauss-Manin systems
arXiv:0712.2021 · doi:10.1016/j.jalgebra.2008.09.010
Abstract
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. and yields a simpler, more algebraic proof. In the process we extend the Euler-Koszul functor a category of infinite toric modules and describe multigraded localizations of Euler-Koszul homology.
15 pages, 1 figure