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Asymptotically Calabi metrics and weak Fano manifolds

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arxiv 2111.09287 v2 pith:ZW2NQWEY submitted 2021-11-17 math.DG math.AGmath.CV

Hans-Joachim Hein , Song Sun , Jeff Viaclovsky , Ruobing Zhang This is my paper · ORCID
classification math.DGmath.AGmath.CV
keywords asymptoticallycalabicalabi-yaufanomanifoldweakanalyticallyapplication
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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.

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  1. Complete Calabi-Yau metrics on noncompact abelian fibered threefolds

    math.DG 2025-01 conditional novelty 7.0 of 10

    Fiber products of two rational elliptic fibrations admit complete Calabi-Yau metrics with ALG/ALH type asymptotics and compactifications with negative canonical class.

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