Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866914740994834432 |
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| author | Bardwell-Evans, Sam Cheung, Man-Wai Mandy Hong, Hansol Lin, Yu-Shen |
| author_facet | Bardwell-Evans, Sam Cheung, Man-Wai Mandy Hong, Hansol Lin, Yu-Shen |
| contents | We construct special Lagrangian fibrations for log Calabi-Yau surfaces, and scattering diagrams from Lagrangian Floer theory of the fibres. Then we prove that the scattering diagrams recover the scattering diagrams of Gross-Pandharipande-Siebert and the canonical scattering diagrams of Gross-Hacking-Keel. With an additional assumption on the non-negativity of boundary divisors, we compute the disc potentials of the Lagrangian torus fibres via a holomorphic/tropical correspondence. As an application, we provide a version of mirror symmetry for rank two cluster varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_15234 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces Bardwell-Evans, Sam Cheung, Man-Wai Mandy Hong, Hansol Lin, Yu-Shen Symplectic Geometry Algebraic Geometry Combinatorics 53D40, 53D37, 13F60 We construct special Lagrangian fibrations for log Calabi-Yau surfaces, and scattering diagrams from Lagrangian Floer theory of the fibres. Then we prove that the scattering diagrams recover the scattering diagrams of Gross-Pandharipande-Siebert and the canonical scattering diagrams of Gross-Hacking-Keel. With an additional assumption on the non-negativity of boundary divisors, we compute the disc potentials of the Lagrangian torus fibres via a holomorphic/tropical correspondence. As an application, we provide a version of mirror symmetry for rank two cluster varieties. |
| title | Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces |
| topic | Symplectic Geometry Algebraic Geometry Combinatorics 53D40, 53D37, 13F60 |
| url | https://arxiv.org/abs/2110.15234 |