Uniform weak RC-positivity and rational connectedness
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917388454199296 |
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| author | Wu, Kuang-Ru |
| author_facet | Wu, Kuang-Ru |
| contents | In this paper, we show that if the holomorphic tangent bundle $TX$ of a compact Kähler 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05981 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniform weak RC-positivity and rational connectedness Wu, Kuang-Ru Differential Geometry Complex Variables In this paper, we show that if the holomorphic tangent bundle $TX$ of a compact Kähler 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. |
| title | Uniform weak RC-positivity and rational connectedness |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2604.05981 |