Mathematical Research Letters

Volume 23 (2016)

Number 3

Hermitian manifolds with semi-positive holomorphic sectional curvature

Pages: 939 – 952

DOI: https://dx.doi.org/10.4310/MRL.2016.v23.n3.a17

Author

Xiaokui Yang (Morningside Center of Mathematics, Institute of Mathematics, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing, China)

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.

Full Text (PDF format)

Accepted 10 December 2015

Published 8 July 2016