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Geometry of logarithmic forms and deformations of complex structures

Kefeng Liu Sheng Rao Xueyuan Wan

Algebraic Geometry mathscidoc:1912.43093

arXiv preprint arXiv:1708.00097, 2017.7
We present a new method to solve certain ar {\partial} -equations for logarithmic differential forms by using harmonic integral theory for currents on Kahler manifolds. The result can be considered as a ar {\partial} -lemma for logarithmic forms. As applications, we generalize the result of Deligne about closedness of logarithmic forms, give geometric and simpler proofs of Deligne's degeneracy theorem for the logarithmic Hodge to de Rham spectral sequences at ar {\partial} -level, as well as certain injectivity theorem on compact Kahler manifolds.
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@inproceedings{kefeng2017geometry,
  title={Geometry of logarithmic forms and deformations of complex structures},
  author={Kefeng Liu, Sheng Rao, and Xueyuan Wan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111510280178653},
  booktitle={arXiv preprint arXiv:1708.00097},
  year={2017},
}
Kefeng Liu, Sheng Rao, and Xueyuan Wan. Geometry of logarithmic forms and deformations of complex structures. 2017. In arXiv preprint arXiv:1708.00097. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111510280178653.
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