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Gromov-Hausdorff limits of collapsing Calabi-Yau fibrations

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arxiv 2505.14939 v1 pith:XUGDA6BV submitted 2025-05-20 math.DG

Gromov-Hausdorff limits of collapsing Calabi-Yau fibrations

G\'abor Sz\'ekelyhidi This is my paper
classification math.DG
keywords calabi-yaufibrationgromov-hausdorffmetricsadditionahlerbaseclass
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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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Cited by 5 Pith papers

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