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

2020/12/01 by Benjamin Bakker, Bakker, Benjamin, Henri Guenancia +3 · 7 citations
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications

paper · doi:10.48550/arxiv.2012.00441

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.

Cited by

• The Cone Conjecture for Primitive Symplectic Varieties over a Field of Characteristic Zero and an Application
• Deformations of primitive Enriques varieties
• Beauville-Bogomolov decomposition for klt varieties
• A note on orbifold regularity of canonical metrics
• Log Calabi--Yau manifolds: holomorphic tensors, stability and universal cover
• Hasse-Schmidt derivations and locally trivial deformations in positive characteristic
• Nonvanishing results for Kähler varieties

Related

• Beauville-Bogomolov decomposition for klt varieties
• A decomposition theorem for smoothable varieties with trivial canonical\n class
• The Calabi conjecture and K-stability
• Stability of algebraic varieties and Kahler geometry
• On structures and discrepancies of klt Calabi--Yau pairs