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arXiv · 2604.05981

Uniform weak RC-positivity and rational connectedness

Kuang-Ru Wu
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Abstract

In this paper, we show that if the holomorphic tangent bundle $TX$ of a compact K\"ahler manifold $X$ is uniformly weakly RC-positive, then $X$ is projective and rationally connected. This result is previously established by Xiaokui Yang under the stronger assumption that $TX$ is uniformly RC-positive. The result we obtain is, in fact, more general. If a holomorphic vector bundle $E$ is uniformly weakly RC-positive, then $E$ admits a Hermitian metric whose mean curvature is positive. A quasi-positive version is also proved in this paper.

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Kuang-Ru Wu. 2026-04-07. Uniform weak RC-positivity and rational connectedness. https://arxiv.org/abs/2604.05981

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