Mellin-Barnes integrals as Fourier-Mukai transforms |
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Authors: | Lev A Borisov R Paul Horja |
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Institution: | a Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA b Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA |
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Abstract: | 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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Keywords: | 14M25 14J32 |
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