Special Lagrangian submanifolds in K3-fibered Calabi-Yau 3-folds

We construct special Lagrangian submanifolds in collapsing Calabi-Yau 3-folds fibered by K3 surfaces. As these 3-folds collapse, the special Lagrangians shrink to 1-dimensional graphs in the base, mirroring the conjectured tropicalization of holomorphic curves in collapsing SYZ torus-fibered Calabi-...

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Bibliographic Details
Published in:arXiv.org 2024-10
Main Authors: Shih-Kai Chiu, Yu-Shen, Lin
Format: Article
Language:English
Subjects:
Lagrangian function
Manifolds (mathematics)
Toruses
Online Access:Get full text
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Summary:We construct special Lagrangian submanifolds in collapsing Calabi-Yau 3-folds fibered by K3 surfaces. As these 3-folds collapse, the special Lagrangians shrink to 1-dimensional graphs in the base, mirroring the conjectured tropicalization of holomorphic curves in collapsing SYZ torus-fibered Calabi-Yau manifolds. This confirms predictions of Donaldson and Donaldson-Scaduto in the Calabi-Yau setting. Additionally, we discuss our results in the contexts of the Thomas-Yau conjecture, the Donaldson-Scaduto conjecture, and mirror symmetry.
ISSN:2331-8422