On compact Kähler manifolds with pseudo-effective tangent bundle

2025/02/02 by Matsumura, Shin-ichi, Qing, Chenghao
#58A30 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Primary 32J25 #Secondary 14F35

paper · doi:10.48550/arxiv.2502.00623

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 ϕ\colon X → 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.

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