Hypergeometric D-modules and twisted Gauss-Manin systems

Details Hypergeometric D-modules and twisted Gauss-Manin systems Hypergeometric D-modules and twisted Gauss-Manin systems

2007-12-12

arxiv.org/abs/0712.2021v3

J. Algebra 322,9 (2009), 3392-3409

Mathematics

Algebraic Geometry

15 pages, 1 figure

Scientific paper

10.1016/j.jalgebra.2008.09.010

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.

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