Mathematical Research Letters
Volume 23 (2016)
Hermitian manifolds with semi-positive holomorphic sectional curvature
Pages: 939 – 952
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.