We study the relationship between solutions to better-behaved GKZ hypergeometric systems near different large radius limit points, and their geometric counterparts given by the $K$-groups of the associated toric Deligne-Mumford stacks. We prove that the $K$-theoretic Fourier-Mukai transforms associated to toric wall-crossing coincide with analytic continuation transformations of Gamma series solutions to the better-behaved GKZ systems, which settles a conjecture of Borisov and Horja.

Comment: 20 pages, 1 figure; published version

• 14J32 - Calabi-Yau manifolds (algebro-geometric aspects)
• 14J33 - Mirror symmetry (algebro-geometric aspects)
• 14M25 - Toric varieties, Newton polyhedra, Okounkov bodies
• 33C99 - Hypergeometric functions