Hermitian manifolds with semi-positive holomorphic sectional curvature

Abstract

We prove that a compact Hermitian manifold with semi-positive but not identically zero holomorphic sectional curvature has Kodaira dimension $-\infty$. As applications, we show that Kodaira surfaces and hyperelliptic surfaces can not admit Hermitian metrics with semi-positive holomorphic sectional curvature although they have nef tangent bundles.

We condense the paper according to the referee's suggestions

References in corpus (7)

• Negative Holomorphic curvature and positive canonical bundle
• An extension of a theorem of Wu-Yau
• Kähler manifolds of semi-negative holomorphic sectional curvature
• On the canonical line bundle and negative holomorphic sectional curvature
• Scalar curvature and uniruledness on projective manifolds
• Big vector bundles and compact complex manifolds with semi-positive tangent bundles
• Optimal pinching for the holomorphic sectional curvature of Hitchin's metrics on Hirzebruch surfaces

Cited by in corpus (1)

• Big vector bundles and compact complex manifolds with semi-positive tangent bundles