Nonexistence for complete Kähler–Einstein metrics on some noncompact manifolds

Article

Abstract

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

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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA
  2. 2.School of Mathematical SciencesTongji UniversityShanghaiChina

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