Abstract
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We introduce the notion of tropical Lagrangian multisections over a fan and study its
relation with toric vector bundles. We also introduce a “SYZ-type” construction for
toric vector bundles which gives a reinterpretation of Kaneyama’s linear algebra data.
In dimension 2, this “mirror-symmetric” approach provides us a pure combinatorial
condition for checking which rank 2 tropical Lagrangian multisections arise from toric
vector bundles.
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Keywords
mirror symmetry, toric geometry, toric vector bundles,
tropical geometry, symplectic geometry, Lagrangian
multisections
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Mathematical Subject Classification
Primary: 14M25, 14Txx
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Milestones
Received: 25 March 2022
Revised: 3 October 2023
Accepted: 3 October 2023
Published: 3 November 2023
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| © 2023 MSP (Mathematical Sciences
Publishers). Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
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