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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{qing2026uniform,
  title = {{Uniform RC-positivity of tangent bundles}},
  author = {Chenghao Qing and Hongzhao Sun and Xiangyu Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27556},
  eprint = {2609.27556},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27556},
}
RIS
TY  - UNPB
TI  - Uniform RC-positivity of tangent bundles
AU  - Chenghao Qing
AU  - Hongzhao Sun
AU  - Xiangyu Zhou
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.27556
UR  - https://arxiv.org/abs/2609.27556
AB  - 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.
ER  -