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arXiv · 2212.13948

Family Floer SYZ singularities for the conifold transition

Hang Yuan
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Abstract

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.

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Hang Yuan. 2022-12-28. Family Floer SYZ singularities for the conifold transition. https://arxiv.org/abs/2212.13948

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