A characterization of uniruled compact Kähler manifolds

2025/01/30 by Ou, Wenhao · 6 citations
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.18088

Abstract

We adapt Bost's algebraicity characterization to the situation of a germ in a compact Kähler manifold. As a consequence, we extend the algebraic integrability criteria of Campana-Păun and of Druel to foliations on compact Kähler manifolds. As an application, we prove that a compact Kähler manifold is uniruled if and only if its canonical line bundle is not pseudoeffective.

Cited by

• Hermitian manifolds with nonpositive holomorphic sectional curvature
• Pluripotential geometry on semi-positive effective divisors of numerical dimension one
• Deformation of nef adjoint canonical line bundles
• Non-algebraicity of non-abundant foliations and abundance for adjoint foliated structures
• Nonvanishing results for Kähler varieties
• Bott-Chern complexity of Kähler pairs

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• Compact Kähler 3-manifolds without non-trivial subvarieties