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

Benjamin Bakker (1) , Henri Guenancia (2, 3) , Christian Lehn (4)

1 UIC - Department of Mathematics, Statistics and Computer Science [Chicago]
2 CNRS - Centre National de la Recherche Scientifique
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 Chemnitz University of Technology / Technische Universität Chemnitz

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.

Mots clés: 2020 Mathematics Subject Classification. 32Q25; 32J27 (primary); 32S15; 32Q20 (secondary) Calabi-Yau variety; decomposition theorem; locally trivial deformation; Kähler-Einstein metric

Domaines: Mathématiques [math]

Benjamin Bakker, Henri Guenancia, Christian Lehn. Algebraic approximation and the decomposition theorem for Kähler Calabi-Yau varieties. 2020. ⟨hal-03035501v1⟩