The crepant transformation conjecture for toric complete intersections

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Title: The crepant transformation conjecture for toric complete intersections
Authors: Coates, T
Iritani, H
Jiang, Y
Item Type: Working Paper
Abstract: Let X and Y be K-equivalent toric Deligne-Mumford stacks related by a single toric wall-crossing. We prove the Crepant Transformation Conjecture in this case, fully-equivariantly and in genus zero. That is, we show that the equivariant quantum connections for X and Y become gauge-equivalent after analytic continuation in quantum parameters. Furthermore we identify the gauge transformation involved, which can be thought of as a linear symplectomorphism between the Givental spaces for X and Y, with a Fourier-Mukai transformation between the K-groups of X and Y, via an equivariant version of the Gamma-integral structure on quantum cohomology. We prove similar results for toric complete intersections. We impose only very weak geometric hypotheses on X and Y: they can be non-compact, for example, and need not be weak Fano or have Gorenstein coarse moduli space. Our main tools are the Mirror Theorems for toric Deligne-Mumford stacks and toric complete intersections, and the Mellin-Barnes method for analytic continuation of hypergeometric functions.
Issue Date: 30-Apr-2018
Copyright Statement: © 2014 The Authors
Keywords: Algebriac geometry
Notes: 61 pages, 3 figures. v2: abstract changed, references updated, remarks added
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences

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