Complex analysis and stability of a polarized manifold

2016 Fiscal Year Final Research Report

• Project/Area Number: 15H06262
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Nagoya University
• Principal Investigator: Hisamoto Tomoyuki 名古屋大学, 多元数理科学研究科, 助教 (00748345)
• Project Period (FY): 2015-08-28 – 2017-03-31
• Keywords: 安定性 / 定スカラー曲率計量 / モンジュ・アンペール方程式 / ベルグマン核

Outline of Final Research Achievements

A fundamental question of differential geometry is whether a complex algebraic manifold in higher dimension admits a canonical metric. In the most natural formalism it is conjectured that a polarized manifold admits a constant scalar curvature Kahler metric if and only if it satisfies a purely algebraic, so-called K-stability condition. We studied more stronger "uniform k-stability" and showed that the it corresponds to the growth condition of the canonical energy functional which characterizes the constant scalar curvature Kahler metric as a critical point. Our study also provides a new approach to the original conjecture.

Free Research Field

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