Non-minimal scalar-flat Kahler surfaces and parabolic stability

• 成果类型: Article
• 署名作者: Rollin, Y; Singer, M
• 署名单位: Massachusetts Institute of Technology (MIT)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-004-0436-6
• 发表日期: 2005
• 页码: 235-270
• 关键词: compact complex-surfaces; self-dual 4-manifolds; vector-bundles; METRICS; SINGULARITIES; CURVATURE; CONSTRUCTION; SPACES

摘要

A new construction is presented of scalar-flat Kahler metrics on non-minimal ruled surfaces. The method is based on the resolution of singularities of orbifold ruled surfaces which are closely related to rank-2 parabolically stable holomorphic bundles. This rather general construction is shown also to give new examples of low genus: in particular, it is shown that CP2 blown up at 10 suitably chosen points, admits a scalar-flat Kahler metric; this answers a question raised by Claude LeBrun in 1986 in connection with the classification of compact self-dual 4-manifolds.