Tropical Lagrangian multi-sections and toric vector bundles

Abstract

We introduce the notion of tropical Lagrangian multi-sections 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, such "mirror-symmetric" approach provides us a pure combinatorial condition for checking which rank 2 tropical Lagrangian multi-section arises from toric vector bundles.

arXiv comment25 pages, 6 figures, comments are welcome. The notion "regularity" is renamed as "separable". Section 4 and 5 is combined. All the results about localization will be moved to another upcoming work. Comments are welcome!

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Cited by in corpus (2)

• Lagrangian multi-sections and their toric equivariant mirror
• Toric vector bundles, non-abelianization, and spectral networks