Constant scalar curvature Kaehler metrics and the stabilty of polarized algebraic manifolds in the geometric invariant theory

几何不变量理论中恒标量曲率凯勒度量与极化代数流形的稳定性

• 批准号: 17540069
• 负责人: NAKAGAWA Yasuhiro
• 金额: $ 1.88万
• 依托单位: Kanazawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17540069/
• 关键词: Einstein-Kaehler metrics; Geometric Invariant Thory; Stablity; Futaki characters; Kaehler-Ricci solitons

We have studied the conjecture which states that the stability of polarized algebraic manifolds in the geometric invariant theory is equivalent to the existence of constant scalar curvature Kaehler metrics on that manifolds, namely "Kobayashi-Hitchin correspondence for polarized algebraic manifolds".In particular, we observed Kaehler-Ricci solitons, which are an generalization of Einstein-Kaehler metrics, from the view points of K-energy, which plays an important role in the research of Einstein-Kaehler metrics, and we could generalize Kaehler-Ricci solitons to the case of general Kaehler classes.Moreover, we have studied the constraction of non-trival examples of this generalized Kaehler-Ricci solitons. Then, we could prove the existence of generalized Kaehler-Ricci solitons for the Kaehler classes, for which the volume of fibers is sufficiently small compare to that of O-section, on the compactification of the holomorphic line bundle over the complex projective line.

我们研究了一个猜想，该猜想指出，几何不变理论中极化代数歧管的稳定性等于存在恒定标量曲率的kaehler kaehler指标，即“ kobayashi-hitchin corterentions”，“ kobayashi-hitchin soliatention for polalgebraic cormitive of pallgebraic歧管”。从K-Energy的角度来看，Einstein-Kaehler的指标在爱因斯坦 - 卡勒勒指标的研究中起着重要作用，我们可以将Kaehler-ricci solitons推广到kaehler类中。然后，我们可以证明在Kaehler类中存在广义的Kaehler-Ricci solitons，在该类别中，纤维的体积与O截面的纤维体积相比足够小，在复杂的投影线上的Holomorthic Line束的紧凑型上。

项目成果

Kahler - Ricci ソリトンの一般化について

关于卡勒-里奇孤子的推广

• 发表时间: 2008
• 作者: Yasuhiro;Hara;中川泰宏
• 通讯作者: 中川泰宏

Kahler・Ricciソリトンの一般化について

关于卡勒-里奇孤子的推广

• 发表时间: 2008
• 作者: Yasuhiro;Hara;中川泰宏;中川 泰宏
• 通讯作者: 中川 泰宏

Critical metrics and K-energy

关键指标和 K 能量

• 发表时间: 2006
• 作者: Yasuhiro;Hara;中川泰宏;中川 泰宏;Y. Nakagawa;Y. Nakagawa;Y. Nakagawa;Y. Nakagawa
• 通讯作者: Y. Nakagawa

On a generalization of Kaehler-Ricci solitons

关于凯勒-里奇孤子的推广

• 发表时间: 2008
• 作者: Yasuhiro;Hara;中川泰宏;中川 泰宏;Y. Nakagawa
• 通讯作者: Y. Nakagawa

K-energy and Critical metrics

K 能量和关键指标

• 发表时间: 2006
• 作者: Yasuhiro;Hara;中川泰宏;中川 泰宏;Y. Nakagawa;Y. Nakagawa;Y. Nakagawa;Y. Nakagawa;Y. Nakagawa
• 通讯作者: Y. Nakagawa