2005/10/23 by Lev Borisov, Borisov, Lev A., R. Paul Horja +1
Mathematics · #14J32 #14M25 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.math/0510486
openalex publication_date 2005/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.