The Gromov-Hausdorff limit of collapsing Calabi-Yau metrics is homeomorphic to the base variety, and the singular set has Hausdorff codimension at least two.
Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below
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Gromov-Hausdorff limits of collapsing Calabi-Yau fibrations
The Gromov-Hausdorff limit of collapsing Calabi-Yau metrics is homeomorphic to the base variety, and the singular set has Hausdorff codimension at least two.