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Collapsing Calabi–Yau fibrations and uniform diameter bounds

Yang Li

Geometry & Topology 27 (2023) 397–415
Abstract

We study Calabi–Yau metrics collapsing along a holomorphic fibration over a Riemann surface. Assuming at worst canonical singular fibres, we prove a uniform diameter bound for all fibres in the suitable rescaling. This has consequences on the geometry around the singular fibres.

Keywords
collapsing, Calabi–Yau, fibration, diameter bound
Mathematical Subject Classification
Primary: 32Q20, 32Q25
Secondary: 32J27
References
Publication
Received: 10 February 2021
Revised: 12 July 2021
Accepted: 6 September 2021
Published: 1 May 2023
Proposed: Gang Tian
Seconded: Simon Donaldson, John Lott
Authors
Yang Li
Department of Mathematics
MIT
Cambridge, MA
United States

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