Hypergeometric D-modules and twisted Gauss-Manin systems

Mathias Schulze; Uli Walther

doi:10.1016/j.jalgebra.2008.09.010

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arXiv · 0712.2021

Hypergeometric D-modules and twisted Gauss-Manin systems

Mathias Schulze·Uli Walther

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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.

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Mathias Schulze, Uli Walther. 2008-09-07. Hypergeometric D-modules and twisted Gauss-Manin systems. https://doi.org/10.1016/j.jalgebra.2008.09.010

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