On compact Kähler manifolds with pseudo-effective tangent bundle
Abstract
Abstract In this paper, we prove that a compact Kähler manifold $X$ with pseudo-effective (resp. singular positively curved) tangent bundle admits a smooth (resp. locally constant) rationally connected fibration $\phi \colon X \to Y$ onto a finite étale quotient $Y$ of a compact complex torus. This result extends the structure theorem previously established for smooth projective varieties to compact Kähler manifolds.
Fields of Study & Subjects
Geometry and complex manifolds
Algebraic Geometry and Number Theory
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 10
- Publication date
- 28 April 2026
- Language
- EN