The J-equation and the supercritical deformed Hermitian-Yang-Mills equation

• 成果类型: Article
• 署名作者: Chen, Gao
• 署名单位: Chinese Academy of Sciences; University of Science & Technology of China, CAS
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01035-3
• 发表日期: 2021
• 页码: 529-602

摘要

In this paper, we prove that for any Kahler metrics omega(0) and chi on M, there exists a Kahler metric omega(phi) = omega(0) + root-1 partial derivative(partial derivative) over bar phi > 0 satisfying the J-equation tr omega(phi)chi = c if and only if (M, [omega(0)], [chi]) is uniformly J-stable. As a corollary, we find a sufficient condition for the existence of constant scalar curvature Kahler metrics with c(1) < 0. Using the same method, we also prove a similar result for the supercritical deformed Hermitian-Yang-Mills equation.