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

2024/10/23 by Chiu, Shih-Kai, Lin, Yu-Shen · 3 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.17662

Abstract

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.

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• Special Lagrangian sections and stability conditions on threefolds
• Log Calabi--Yau manifolds: holomorphic tensors, stability and universal cover
• From tropical curves to special Lagrangians

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