Nonexistence for complete KhlerEinstein metrics on some noncompact manifolds

Peng Gao Shing-Tung Yau Wubin Zhou

Algebraic Geometry mathscidoc:1912.43680

Mathematische Annalen, 369, 1271-1282, 2017.12
Let <i>M</i> be a compact Khler manifold and <i>N</i> be a subvariety with codimension greater than or equal to 2. We show that there are no complete KhlerEinstein metrics on M - N . As an application, let <i>E</i> be an exceptional divisor of <i>M</i>. Then M - N cannot admit any complete KhlerEinstein metric if blow-down of <i>E</i> is a complex variety with only canonical or terminal singularities. A similar result is shown for pairs.
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@inproceedings{peng2017nonexistence,
  title={Nonexistence for complete KhlerEinstein metrics on some noncompact manifolds},
  author={Peng Gao, Shing-Tung Yau, and Wubin Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204935583248244},
  booktitle={Mathematische Annalen},
  volume={369},
  pages={1271-1282},
  year={2017},
}
Peng Gao, Shing-Tung Yau, and Wubin Zhou. Nonexistence for complete KhlerEinstein metrics on some noncompact manifolds. 2017. Vol. 369. In Mathematische Annalen. pp.1271-1282. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204935583248244.
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