Complete Calabi-Yau metrics on noncompact K3 fibered threefolds

Abstract

In this article, we construct complete Calabi--Yau metrics on Lefschetz K3 fibrations over $\mathbb{C}$. Our approach involves a gluing construction for a collapsing approximate metric, followed by a perturbation argument. These Calabi--Yau metrics have linear volume growth, unbounded sectional curvature, and are Gromov--Hausdorff asymptotic to a product $\mathbb{R}\times Z$, where $Z$ is a compact singular metric space.

73 pages. Typos corrected. Some improvements to the presentation