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@article{Coates:2018:10.1016/j.aim.2017.11.017,
author = {Coates, TH and Iritani, H and Jiang, Y},
doi = {10.1016/j.aim.2017.11.017},
journal = {Advances in Mathematics},
pages = {1002--1087},
title = {The Crepant Transformation Conjecture for toric complete intersections},
url = {http://dx.doi.org/10.1016/j.aim.2017.11.017},
volume = {329},
year = {2018}
}

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TY  - JOUR
AB  - 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.
AU  - Coates,TH
AU  - Iritani,H
AU  - Jiang,Y
DO  - 10.1016/j.aim.2017.11.017
EP  - 1087
PY  - 2018///
SN  - 0001-8708
SP  - 1002
TI  - The Crepant Transformation Conjecture for toric complete intersections
T2  - Advances in Mathematics
UR  - http://dx.doi.org/10.1016/j.aim.2017.11.017
UR  - https://www.sciencedirect.com/science/article/pii/S0001870817303420
UR  - http://hdl.handle.net/10044/1/53706
VL  - 329
ER  -

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