On the image of MRC fibrations of projective manifolds with semi-positive holomorphic sectional curvature

Abstract

In this paper, we pose several conjectures on structures and images of maximal rationally connected fibrations of smooth projective varieties admitting semi-positive holomorphic sectional curvature. Toward these conjectures, we prove that the canonical bundle of images of such fibrations is not big. Our proof gives a generalization of Yang's solution using RC positivity for Yau's conjecture. As an application, we show that any compact Kähler surface with semi-positive holomorphic sectional curvature is rationally connected, or a complex torus, or a ruled surface over an elliptic curve.

16pages, v2: completely revised

References in corpus (2)

• A partial converse to the Andreotti-Grauert theorem
• RC-positivity, rational connectedness and Yau's conjecture

Cited by in corpus (7)

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• RC-positive metrics on rationally connected manifolds
• On morphisms of compact Kähler manifolds with semi-positive holomorphic sectional curvature
• Compact Kähler manifolds with quasi-positive second Chern-Ricci curvature
• Structure of projective varieties with nef anticanonical divisor: the case of log terminal singularities
• Positive curvature operator, projective manifold and rational connectedness
• Deformation of Hermitian metrics