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

Chunle Huang Kefeng Liu Xueyuan Wan 杨晓奎 MCM, CAS

mathscidoc:1703.01001

In this paper, we first establish an $L^2$-type Dolbeault isomorphism for logarithmic differential forms by H\"{o}rmander's $L^2$-estimates. By using this isomorphism and the construction of smooth Hermitian metrics, we obtain a number of new %Akizuki-Kodaira-Nakano type vanishing theorems for sheaves of logarithmic differential forms on compact K\"ahler 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.
vanishing theorem
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@inproceedings{chunlelogarithmic,
  title={Logarithmic vanishing theorems on compact K\"{a}hler manifolds I},
  author={Chunle Huang, Kefeng Liu, Xueyuan Wan, and 杨晓奎},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170307201423212026620},
}
Chunle Huang, Kefeng Liu, Xueyuan Wan, and 杨晓奎. Logarithmic vanishing theorems on compact K\"{a}hler manifolds I. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170307201423212026620.
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