Nonexistence for complete Kähler Einstein metrics on some noncompact manifolds

2016/03/30 by Peng Gao, Gao, Peng, Shing-Tung Yau +4
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1603.09135

arxiv created 2016/03/30 · openalex publication_date 2016/03/30 · arxiv updated 2016/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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