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Logarithmic vanishing theorems on compact K\"{a} hler manifolds I

Chunle Huang Kefeng Liu Xueyuan Wan Xiaokui Yang

Algebraic Geometry mathscidoc:1912.43101

arXiv preprint arXiv:1611.07671, 2016.11
In this paper, we first establish an L^ 2-type Dolbeault isomorphism for logarithmic differential forms by Hrmander's L^ 2-estimates. By using this isomorphism and the construction of smooth Hermitian metrics, we obtain a number of new vanishing theorems for sheaves of logarithmic differential forms on compact Khler manifolds with simple normal crossing divisors, which generalize several classical vanishing theorems, including Norimatsu's vanishing theorem, Gibrau's vanishing theorem, Le Potier's vanishing theorem and a version of the Kawamata-Viehweg vanishing theorem.
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@inproceedings{chunle2016logarithmic,
  title={Logarithmic vanishing theorems on compact K\"{a} hler manifolds I},
  author={Chunle Huang, Kefeng Liu, Xueyuan Wan, and Xiaokui Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111542117126661},
  booktitle={arXiv preprint arXiv:1611.07671},
  year={2016},
}
Chunle Huang, Kefeng Liu, Xueyuan Wan, and Xiaokui Yang. Logarithmic vanishing theorems on compact K\"{a} hler manifolds I. 2016. In arXiv preprint arXiv:1611.07671. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111542117126661.
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