Conjecture 1.1 . [03Y3]
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Conjecture 1.1.
[26][16] Let be a degenerating family of (polarized) Calabi-Yau 3-folds near the large complex structure limit, equipped with Calabi-Yau metrics . Then for , the 3-fold admits a special Lagrangian -fibration over a base homeomorphic to a 3-sphere, known as the SYZ fibration. The base is equipped with an affine structure and a compatible metric solving the real Monge-Ampère equation with singularities along a trivalent graph , such that the rescaled Calabi-Yau metrics converge to in Gromov-Hausdorff sense as . Morever, suitably away from the metrics are approximated by a semiflat metric up to exponentially small errors.