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Asymptotically Calabi
metrics and weak Fano manifolds
Hans-Joachim Hein, Song Sun, Jeffrey Viaclovsky and Ruobing Zhang |
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Geometry & Topology 29 (2025) 2547–2569
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Abstract |
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We show that any asymptotically Calabi manifold which is Calabi–Yau can be compactified complex analytically to a weak Fano manifold. Furthermore, the Calabi–Yau structure arises from a generalized Tian–Yau construction on the compactification, and we prove a strong uniqueness theorem. We also give an application of this result to the surface case. |
Keywords
Calabi–Yau, weak Fano manifold, complex compactification
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Mathematical Subject Classification
Primary: 53C21, 53C25, 53C55
Secondary: 14J32, 14J45
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References |
Publication
Received: 12 September 2023
Revised: 19 July 2024
Accepted: 14 September 2024
Published: 14 August 2025
Proposed: Simon Donaldson
Seconded: Tobias H Colding, Mark Gross
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Authors |
| Hans-Joachim Hein | |
| Mathematisches Institut Universität Münster Münster Germany |
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| Song Sun | |
| Institute for Advanced Study in
Mathematics Zhejiang University Hangzhou China |
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| Jeffrey Viaclovsky | |
| Department of Mathematics University of California, Irvine Irvine, CA United States |
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| Ruobing Zhang | |
| Department of Mathematics University of California San Diego, CA United States |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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