Family Floer SYZ singularities for the conifold transition
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.
Keywords
Cite
@article{arxiv.2212.13948,
title = {Family Floer SYZ singularities for the conifold transition},
author = {Hang Yuan},
journal= {arXiv preprint arXiv:2212.13948},
year = {2025}
}
Comments
24 pages. Accepted version. To provide further clarity, an outline of the construction has been added to the introduction, particularly addressing some concerns about the matching of integral affine structures