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Lagrangian multi-sections and their toric equivariant mirror

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Title
Lagrangian multi-sections and their toric equivariant mirror
Author(s)
Yong-Geun Oh; Yat-Hin Suen
Publication Date
2024-04
Journal
Advances in Mathematics, v.441
Publisher
Academic Press Inc.
Abstract
The SYZ conjecture suggests a folklore that “Lagrangian multi-sections are mirror to holomorphic vector bundles”. In this paper, we prove this folklore for Lagrangian multi-sections inside the cotangent bundle of a vector space, which are equivariantly mirror to complete toric varieties by the work of Fang-Liu-Treumann-Zaslow. We also introduce the Lagrangian realization problem, which asks whether one can construct an unobstructed Lagrangian multi-section with asymptotic conditions prescribed by a tropical Lagrangian multi-section. We solve the realization problem for tropical Lagrangian multi-sections over a complete 2-dimensional fan that satisfy the so-called N-generic condition. As an application, we show that every rank 2 toric vector bundle on the projective plane is mirror to a Lagrangian multi-section. © 2024 Elsevier Inc.
URI
https://pr.ibs.re.kr/handle/8788114/14974
DOI
10.1016/j.aim.2024.109545
ISSN
0001-8708
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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