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Homological mirror
symmetry for hypertoric varieties, II
Benjamin Gammage, Michael McBreen and Ben WebsterAppendix: Benjamin Gammage, Michael McBreen, Ben Webster, Laurent Côté and Justin Hilburn |
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Geometry & Topology 29 (2025) 3921–3993
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Abstract |
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We prove a homological mirror symmetry equivalence for pairs of multiplicative hypertoric varieties, and we calculate monodromy autoequivalences of these categories by promoting our result to an equivalence of perverse schobers. We prove our equivalence by matching holomorphic Lagrangian skeleta, on the A-model side, with noncommutative resolutions on the B-model side. The hyperkähler geometry of these spaces provides each category with a natural t-structure, which helps clarify SYZ duality in a hyperkähler context. Our results are a prototype for mirror symmetry statements relating pairs of K-theoretic Coulomb branches. |
Keywords
homological mirror symmetry, multiplicative hypertoric
varieties, Fukaya categories, perverse Schobers
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Mathematical Subject Classification 2010
Primary: 14J33, 53D37
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References |
Publication
Received: 17 October 2019
Revised: 5 March 2025
Accepted: 15 April 2025
Published: 26 November 2025
Proposed: András I Stipsicz
Seconded: Jim Bryan, Mark Gross
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Authors |
| Benjamin Gammage | |
| Department of Mathematics Harvard University Cambridge, MA United States |
Department of Mathematics University of Toronto Toronto, ON Canada |
| Michael McBreen | |
| Department of Mathematics Chinese University of Hong Kong Hong Kong |
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| Ben Webster | |
| Department of Pure Mathematics University of Waterloo Waterloo, ON Canada |
Perimeter Institute for Theoretical
Physics Waterloo, ON Canada |
| Laurent Côté | |
| Mathematical Institute University of Bonn Bonn Germany |
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| Justin Hilburn | |
| Perimeter Institute for Theoretical
Physics Waterloo, ON Canada |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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