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arXiv · 2111.09287

Asymptotically Calabi metrics and weak Fano manifolds

Hans-Joachim Hein·Song Sun·Jeff Viaclovsky·Ruobing Zhang
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Abstract

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.

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Hans-Joachim Hein, Song Sun, Jeff Viaclovsky, Ruobing Zhang. 2021-11-17. Asymptotically Calabi metrics and weak Fano manifolds. https://doi.org/10.2140/gt.2025.29.2547

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