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

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arxiv 2410.17662 v1 pith:F7PCHIBG submitted 2024-10-23 math.DG

Shih-Kai Chiu , Yu-Shen Lin This is my paper · ORCID
classification math.DG
keywords calabi-yaufoldsspecialcollapsingconjecturedonaldson-scadutolagrangiansubmanifolds
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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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  1. Log Calabi--Yau manifolds: holomorphic tensors, stability and universal cover

    math.AG 2025-09 conditional novelty 8.0 of 10

    For log Calabi-Yau pairs, a smooth boundary gives holonomy SU(n), Bochner principle, and stability, while two boundary components break all three and make the universal cover non-compactifiable.

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