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arXiv · 1412.5252

Hermitian manifolds with semi-positive holomorphic sectional curvature

Xiaokui Yang
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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.

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Xiaokui Yang. 2014-12-17. Hermitian manifolds with semi-positive holomorphic sectional curvature. https://arxiv.org/abs/1412.5252

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