Algebraic approximation and the decomposition theorem for K\"ahler Calabi-Yau varieties

TL;DR

This paper extends the decomposition theorem to K"ahler Calabi-Yau varieties with singularities and proves they admit strong algebraic approximations, advancing the understanding of their structure and classification.

Contribution

It generalizes the decomposition theorem to the K"ahler setting and confirms a conjecture by showing all such varieties have strong algebraic approximations.

Findings

Extended the decomposition theorem to K"ahler Calabi-Yau varieties.

Proved all such varieties admit strong locally trivial algebraic approximations.

Completed the numerically $K$-trivial case of Campana and Peternell's conjecture.

Abstract

We extend the decomposition theorem for numerically $K$-trivial varieties with log terminal singularities to the K\"ahler setting. Along the way we prove that all such varieties admit a strong locally trivial algebraic approximation, thus completing the numerically $K$-trivial case of a conjecture of Campana and Peternell.