Lagrangian multi-section and their toric equivariant mirror
SCIE
SCOPUS
- Title
- Lagrangian multi-section and their toric equivariant mirror
- Authors
- OH, YONG GEUN; Suen, Marco Yat-Hin
- Date Issued
- 2024-04
- Publisher
- Academic Press
- 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 2-fold tropical Lagrangian multi-sections over a complete 2-dimensional fan that satisfy the so-called $N$-generic condition with $N\geq 3$. As an application, we show that every rank 2 toric vector bundle on the projective plane is mirror to a Lagrangian multi-section.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/123603
- DOI
- 10.1016/j.aim.2024.109545
- ISSN
- 0001-8708
- Article Type
- Article
- Citation
- Advances in Mathematics, 2024-04
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- There are no files associated with this item.
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