Algebraic approximation and the decomposition theorem for Kähler Calabi-Yau varieties

Abstract

We extend the decomposition theorem for numerically $K$-trivial varieties with log terminal singularities to the Kähler 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.

arXiv commentv2: Minor inaccuracies corrected, main results unchanged. v3: Exposition improved, final version, to appear in Invent. Math