Special Lagrangian submanifolds in K3-fibered Calabi-Yau 3-folds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913560976687104 |
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| author | Chiu, Shih-Kai Lin, Yu-Shen |
| author_facet | Chiu, Shih-Kai Lin, Yu-Shen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Special Lagrangian submanifolds in K3-fibered Calabi-Yau 3-folds Chiu, Shih-Kai Lin, Yu-Shen Differential Geometry 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. |
| title | Special Lagrangian submanifolds in K3-fibered Calabi-Yau 3-folds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2410.17662 |