Asymptotically Calabi metrics and weak Fano manifolds

TL;DR

This paper demonstrates that asymptotically Calabi Calabi-Yau manifolds can be compactified into weak Fano manifolds, with the Calabi-Yau structure arising from a generalized Tian-Yau construction, and establishes a strong uniqueness result.

Contribution

It establishes a link between asymptotically Calabi Calabi-Yau manifolds and weak Fano compactifications, introducing a generalized Tian-Yau construction and proving a uniqueness theorem.

Findings

Compactification of asymptotically Calabi Calabi-Yau manifolds into weak Fano manifolds.

Calabi-Yau structures derived from a generalized Tian-Yau construction.

Strong uniqueness theorem for the compactification and structure.

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.