Uniform RC-positivity of tangent bundles

Chenghao Qing; Hongzhao Sun; Xiangyu Zhou

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arXiv · 2609.27556

Uniform RC-positivity of tangent bundles

Chenghao Qing·Hongzhao Sun·Xiangyu Zhou

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Abstract

In this paper, we prove that every rationally connected projective manifold admits a smooth uniformly RC-positive Hermitian metric on its tangent bundle, answering Yang's question and giving a characterization of rational connectedness by uniform RC-positivity. We find an example to show that RC-positivity alone does not characterize rational connectedness. We also prove that uniform RC-positivity of the tangent bundle is preserved under blow-ups along connected smooth centers on compact complex manifolds. In the non-Kähler setting, we construct such metrics on all Hopf and Kato surfaces and obtain classification results for compact complex surfaces.

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BibTeX RIS

Chenghao Qing, Hongzhao Sun, Xiangyu Zhou. 2026-09-23. Uniform RC-positivity of tangent bundles. https://arxiv.org/abs/2609.27556

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