Mellin-Barnes integrals as Fourier-Mukai transforms
Algebraic Geometry
2007-05-23 v1 High Energy Physics - Theory
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 -theory of the associated DM stacks. In the spirit of the homological mirror symmetry conjecture of Kontsevich, we show that the -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.
Cite
@article{arxiv.math/0510486,
title = {Mellin-Barnes integrals as Fourier-Mukai transforms},
author = {Lev A. Borisov and R. Paul Horja},
journal= {arXiv preprint arXiv:math/0510486},
year = {2007}
}
Comments
55 pages, LaTeX