Nonexistence for complete K\"ahler Einstein metrics on some noncompact manifolds

Peng Gao; Shing-Tung Yau; Wubin Zhou

Nonexistence for complete K\"ahler Einstein metrics on some noncompact manifolds

Differential Geometry 2016-03-31 v1

Authors: Peng Gao , Shing-Tung Yau , Wubin Zhou

Abstract

Let $M$ be a compact K\"ahler manifold and $N$ be a subvariety with codimension greater than or equal to 2. We show that there are no complete K\"ahler--Einstein metrics on $M-N$ . As an application, let $E$ be an exceptional divisor of $M$ . Then $M-E$ cannot admit any complete K\"ahler--Einstein metric if blow-down of $E$ is a complex variety with only canonical or terminal singularities. A similar result is shown for pairs.

Keywords

kähler metrics einstein metrics kähler manifolds

Cite

@article{arxiv.1603.09135,
  title  = {Nonexistence for complete K\"ahler Einstein metrics on some noncompact manifolds},
  author = {Peng Gao and Shing-Tung Yau and Wubin Zhou},
  journal= {arXiv preprint arXiv:1603.09135},
  year   = {2016}
}

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