Gromov-Hausdorff limits of collapsing Calabi-Yau fibrations
arXiv:2505.14939
Abstract
We study Calabi-Yau metrics on a projective manifold in Kähler classes converging to a semiample class given by a fibration. We show that the Gromov-Hausdorff limit of the metrics is homeomorphic to the base of the fibration and in addition the discriminant locus has Hausdorff codimension at least 2. This resolves conjectures of Tosatti.
18 pages