Abstract
We study Givental’s Lagrangian cone for the quantum orbifold cohomology of toric stack bundles. Using Gromov–Witten invariants of the base and combinatorics of the toric stack fibers, we construct an explicit slice of the Lagrangian cone defined by the genus 0 Gromov–Witten theory of a toric stack bundle.
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Notes
In the presence of a torus action, we may allow \(\mathcal {X}\) to be only semi-projective.
We abuse notation here: \(\mathcal {P}_{\sigma }\) are gerbes over B which may not have sections.
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Acknowledgements
We thank the referees for valuable comments and suggestions. H.-H. T. thanks T. Coates, A. Corti, and H. Iritani for related collaborations. Y. J. thanks T. Coates, A. Corti and R. Thomas for the support at Imperial College London. Y. J. and H.-H. T. are supported in part by Simons Foundation Collaboration Grants. F. Y. was supported by a Presidential Fellowship of the Ohio State University during the revision of this paper.
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Jiang, Y., Tseng, HH. & You, F. The quantum orbifold cohomology of toric stack bundles. Lett Math Phys 107, 439–465 (2017). https://doi.org/10.1007/s11005-016-0903-1
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DOI: https://doi.org/10.1007/s11005-016-0903-1