The research demonstrates Gromov-Hausdorff limits in Calabi-Yau metrics, resolving Tosatti's conjectures on semiample classes and codimension.
We study Calabi-Yau metrics on a projective manifold in K\"ahler 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.
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Gábor Székelyhidi (2025) studied this question.
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