English

Asymptotically Calabi metrics and weak Fano manifolds

Differential Geometry 2025-08-20 v2 Algebraic Geometry Complex Variables

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.

Keywords

Cite

@article{arxiv.2111.09287,
  title  = {Asymptotically Calabi metrics and weak Fano manifolds},
  author = {Hans-Joachim Hein and Song Sun and Jeff Viaclovsky and Ruobing Zhang},
  journal= {arXiv preprint arXiv:2111.09287},
  year   = {2025}
}