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Positivity and vanishing theorems for ample vector bundles

Kefeng Liu Xiaofeng Sun Xiaokui Yang

Differential Geometry mathscidoc:1912.43063

arXiv preprint arXiv:1006.1465, 2010.6
In this paper, we study the Nakano-positivity and dual-Nakano-positivity of certain adjoint vector bundles associated to ample vector bundles. As applications, we get new vanishing theorems about ample vector bundles. For example, we prove that if E is an ample vector bundle over a compact Khler manifold E , $ S^ kE\ts\det E $ is both Nakano-positive and dual-Nakano-positive for any E . Moreover, $ H^{n, q}(X, S^ kE\ts\det E)= H^{q, n}(X, S^ kE\ts\det E)= 0$ for any E . In particular, if E is a Griffiths-positive vector bundle, the naturally induced Hermitian vector bundle $(S^ kE\ts\det E, S^ kh\ts\det h) $ is both Nakano-positive and dual-Nakano-positive for any E .
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@inproceedings{kefeng2010positivity,
  title={Positivity and vanishing theorems for ample vector bundles},
  author={Kefeng Liu, Xiaofeng Sun, and Xiaokui Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111330905099623},
  booktitle={arXiv preprint arXiv:1006.1465},
  year={2010},
}
Kefeng Liu, Xiaofeng Sun, and Xiaokui Yang. Positivity and vanishing theorems for ample vector bundles. 2010. In arXiv preprint arXiv:1006.1465. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111330905099623.
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