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}
}