Chern number identities on compact complex surfaces and applications

Xiaokui Yang

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arXiv · 2508.11171

Chern number identities on compact complex surfaces and applications

Xiaokui Yang

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Abstract

In this paper, we establish Chern number identities on compact complex surfaces. As an application, we prove that if $(M,g)$ is a compact Riemannian four-manifold with constant scalar curvature and admits a compatible complex structure $J$ such that the complexified Ricci curvature is a non-positive $(1,1)$ form, then $M$ is a K\"ahler surface.

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Xiaokui Yang. 2025-08-15. Chern number identities on compact complex surfaces and applications. https://arxiv.org/abs/2508.11171

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