GIT stability of polarized algebraic manifolds

2014 Fiscal Year Final Research Report

• Project/Area Number: 23740063
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Tokyo Institute of Technology (2013-2014); Ritsumeikan University (2011-2012)
• Principal Investigator: NITTA Yasufumi 東京工業大学, 理工学研究科, 助教 (90581596)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: GIT安定性 / 定スカラー曲率ケーラー計量 / 漸近的Chow安定性 / 強K-安定性 / 端的ケーラー計量

Outline of Final Research Achievements

Firstly, we proved that strong relative K-stability of polarized algebraic manifolds implied asymptotic relative Chow-stability. In particular, as a special case, we see that asymptotic Chow-stability follows from strong K-stability.
Next, we showed the uniqueness of Sasaki-Einstein metrics on compact Sasaki　manifolds modulo the action of the identity component of the automorphism group for　the transverse holomorphic structure. Also, we obtain a Myers' type theorem for complete Sasaki manifolds with positive transverse Ricci curvature.

Free Research Field

複素微分幾何学