Family Floer SYZ singularities for the conifold transition
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866910913641054208 |
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| author | Yuan, Hang |
| author_facet | Yuan, Hang |
| contents | We show a mathematically precise version of the SYZ conjecture, proposed in the family Floer context, for the conifold with a conjectural mirror relation between smoothing and crepant resolution. The singular T-duality fibers are explicitly written and exactly correspond to the codimension-2 `missing points' in the mirror cluster variety, which confirms the speculation of Chan, Pomerleano, and Ueda but only in the non-archimedean setting. Concerning purely the area of Berkovich geometry and forgetting all the mirror symmetry background, our B-side analytic fibration is also a new explicit example of affinoid torus fibration with singular extension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_13948 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Family Floer SYZ singularities for the conifold transition Yuan, Hang Symplectic Geometry Mathematical Physics Algebraic Geometry Differential Geometry We show a mathematically precise version of the SYZ conjecture, proposed in the family Floer context, for the conifold with a conjectural mirror relation between smoothing and crepant resolution. The singular T-duality fibers are explicitly written and exactly correspond to the codimension-2 `missing points' in the mirror cluster variety, which confirms the speculation of Chan, Pomerleano, and Ueda but only in the non-archimedean setting. Concerning purely the area of Berkovich geometry and forgetting all the mirror symmetry background, our B-side analytic fibration is also a new explicit example of affinoid torus fibration with singular extension. |
| title | Family Floer SYZ singularities for the conifold transition |
| topic | Symplectic Geometry Mathematical Physics Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2212.13948 |