Blowing up Kahler manifolds with constant scalar curvature, II

• 成果类型: Article
• 署名作者: Arezzo, Claudio; Pacard, Frank
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.170.685
• 发表日期: 2009
• 页码: 685-738
• 关键词: einstein metrics; deformation-theory; complex-surfaces; EXISTENCE; STABILITY

摘要

In this paper we prove the existence of Kahler metrics of constant scalar curvature on the blow up at finitely many points of a compact manifold that already carries a constant scalar curvature Kahler metric. In the case where the manifold has nontrivial holomorphic vector fields with zeros, we give necessary conditions on the number and locations of the blow up points for the blow up to carry constant scalar curvature Kahler metrics.