Blowing up extremal Kahler manifolds II

• 成果类型: Article
• 署名作者: Szekelyhidi, Gabor
• 署名单位: University of Notre Dame
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0543-y
• 发表日期: 2015
• 页码: 925-977
• 关键词: constant scalar curvature; METRICS; STABILITY; EXISTENCE

摘要

This is a continuation of the work of Arezzo-Pacard-Singer and the author on blowups of extremal Kahler manifolds. We prove the conjecture stated in Sz,kelyhidi (Duke Math J 161(8):1411-1453, 2012), and we relate this result to the K-stability of blown up manifolds. As an application we prove that if a Kahler manifold of dimension 2 admits a constant scalar curvature (cscK) metric, then the blowup of at a point admits a cscK metric if and only if it is K-stable, as long as the exceptional divisor is sufficiently small.