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Hypergeometric D-modules and twisted Gauß-Manin systems. (English) Zbl 1181.13023
Summary: 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 I. M. Gelfand, M. M. Kapranav, and A. Y. Zelevinskij [Adv. Math. 84, No. 2, 255–271 (1990; Zbl 0741.33011), 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.

13N10 Commutative rings of differential operators and their modules
33C70 Other hypergeometric functions and integrals in several variables
16E05 Syzygies, resolutions, complexes in associative algebras
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