RC-positivity, vanishing theorems and rigidity of holomorphic maps

Xiaokui Yang Department of Mathematics and Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China

Complex Variables and Complex Analysis Differential Geometry Algebraic Geometry mathscidoc:2206.08001

Journal of the Institute of Mathematics of Jussieu, 20, (3), 2019.10
Let M and N be two compact complex manifolds. We show that if the tautological line bundle O_{T^∗}M(1) is not pseudo-effective and O_{T^∗}N(1) is nef, then there is no non-constant holomorphic map from M to N. In particular, we prove that any holomorphic map from a compact complex manifold M with RC-positive tangent bundle to a compact complex manifold N with nef cotangent bundle must be a constant map. As an application, we obtain that there is no non-constant holomorphic map from a compact Hermitian manifold with positive holomorphic sectional curvature to a Hermitian manifold with non-positive holomorphic bisectional curvature.
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@inproceedings{xiaokui2019rc-positivity,,
  title={RC-positivity, vanishing theorems and rigidity of holomorphic maps},
  author={Xiaokui Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220622154817770728449},
  booktitle={Journal of the Institute of Mathematics of Jussieu},
  volume={20},
  number={3},
  year={2019},
}
Xiaokui Yang. RC-positivity, vanishing theorems and rigidity of holomorphic maps. 2019. Vol. 20. In Journal of the Institute of Mathematics of Jussieu. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220622154817770728449.
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