Hyperdiscriminant polytopes, Chow polytopes, and Mabuchi energy asymptotics

• 成果类型: Article
• 署名作者: Paul, Sean Timothy
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2012.175.1.7
• 发表日期: 2012
• 页码: 255-296
• 关键词: kahler-einstein metrics; bott-chern forms

摘要

Let X-n -> P-N be a smooth, linearly normal algebraic variety. It is shown that the Mabuchi energy of (X, omega(FS vertical bar X)) restricted to the Bergman metrics is completely determined by the X-hyperdiscriminant of format (n - 1) and the Chow form of X. As a corollary it is shown that the Mabuchi energy is bounded from below for all degenerations in G if and only if the hyperdiscriminant polytope dominates the Chow polytope for all maximal algebraic tori H of G.