Mellin-Barnes integrals as Fourier-Mukai transforms

Details Mellin-Barnes integrals as Fourier-Mukai transforms Mellin-Barnes integrals as Fourier-Mukai transforms

2005-10-23

arxiv.org/abs/math/0510486v1

Mathematics

Algebraic Geometry

55 pages, LaTeX

Scientific paper

We study the generalized hypergeometric system introduced by Gelfand, Kapranov and Zelevinsky and its relationship with the toric Deligne-Mumford (DM) stacks recently studied by Borisov, Chen and Smith. We construct series solutions with values in a combinatorial version of the Chen-Ruan (orbifold) cohomology and in the $K$-theory of the associated DM stacks. In the spirit of the homological mirror symmetry conjecture of Kontsevich, we show that the $K$-theory action of the Fourier-Mukai functors associated to basic toric birational maps of DM stacks are mirrored by analytic continuation transformations of Mellin-Barnes type.

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