Crepant Transformation Correspondence For Toric Stack Bundles

Abstract

We prove a crepant transformation correspondence in genus zero Gromov-Witten theory for toric stack bundles related by crepant wall-crossings of the toric fibers. Specifically, we construct a symplectic transformation that identifies $I$-functions toric stack bundles suitably analytically continued using Mellin-Barnes integral approach. We compare our symplectic transformation with a Fourier-Mukai isomorphism between the $K$-groups.

25 pages, preliminary version, comments very welcome; v2: 25 pages, revision to appear in Advances in Geometry

References in corpus (7)

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• The orbifold Chow ring of toric Deligne-Mumford stacks
• Computing Genus-Zero Twisted Gromov-Witten Invariants
• A Mirror Theorem for Toric Stacks
• The Crepant Transformation Conjecture for Toric Complete Intersections
• K-Theoretic and Categorical Properties of Toric Deligne--Mumford Stacks
• The Quantum Orbifold Cohomology of Toric Stack Bundles