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March 2021 On collapsing Calabi–Yau fibrations
Yang Li
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J. Differential Geom. 117(3): 451-483 (March 2021). DOI: 10.4310/jdg/1615487004

Abstract

We develop some techniques to study the adiabatic limiting behaviour of Calabi–Yau metrics on the total space of a fibration, and obtain strong control near the singular fibres by imposing restrictions on the singularity types. We prove a uniform lower bound on the metric up to the singular fibre, under fairly general hypotheses. Assuming a result in pluripotential theory, we prove a uniform fibre diameter bound for a Lefschetz K3 fibred Calabi–Yau $3$‑fold, which reduces the study of the collapsing metric to a locally non-collapsed situation, and we identify the Gromov–Hausdorff limit of the rescaled neighbourhood of the singular fibre.

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Yang Li. "On collapsing Calabi–Yau fibrations." J. Differential Geom. 117 (3) 451 - 483, March 2021. https://doi.org/10.4310/jdg/1615487004

Information

Received: 4 December 2017; Published: March 2021
First available in Project Euclid: 11 March 2021

Digital Object Identifier: 10.4310/jdg/1615487004

Rights: Copyright © 2021 Lehigh University

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Vol.117 • No. 3 • March 2021
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