Complete Calabi-Yau metrics on noncompact abelian fibered threefolds

TL;DR

This paper constructs complete Calabi-Yau metrics on noncompact abelian fibered threefolds over complex numbers and provides a compactification with a negative canonical bundle.

Contribution

It introduces a method to construct complete Calabi-Yau metrics on abelian fibered threefolds and achieves a compactification with negative canonical bundle.

Findings

Successfully constructed complete Calabi-Yau metrics on the specified threefolds.

Provided a compactification with negative canonical bundle.

Advances understanding of noncompact Calabi-Yau geometries.

Abstract

In this article, we construct complete Calabi-Yau metrics on abelian fibrations $X$ over $\mathbb{C}$. We also provide compactification for $X$ so that the compactified variety has negative canonical bundle.