Extremal measures on compact Kahler manifolds
Project/Area Number |
15K04853
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | Sophia University |
Principal Investigator |
TSUJI HAJIME 上智大学, 理工学部, 教授 (30172000)
|
Project Period (FY) |
2015-04-01 – 2018-03-31
|
Project Status |
Completed (Fiscal Year 2017)
|
Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
Keywords | ケーラー・リッチ流 / ケーラー・アインシュタイン計量 / 多重劣調和関数 / 特異エルミート計量 / 正閉カレント / ケーラー多様体 / 随伴直線束 / 射影代数多様体 / 標準系 / 複素多様体の変形 / モジュライ空間 / 擬凸性 / ベルグマン核 / 射影族 / ケーラー族 / モンジュ・アンペール方程式 / 粘性解 / 多重種数 / 極値的測度 |
Outline of Final Research Achievements |
We prove that tha Kaehler-Ricci flow on a projective manifold with abundaant canonical bundle has a long time current solution and the limit is tha curvature current of the canonical measure. Also we prove an inequality for Kaehler-Einstein volume forms on algebraic fiber spaces. Namely we prove that the K-E volume form on the total space is bigger than or equal to the product of the relative K-E volume form and pullback of the K-E volume form on the base space. We have also proven the simliar inequalty for the Bergman volume forms (for the adjoint line bundles) on the algebraic fiber sace.
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Report
(4 results)
Research Products
(10 results)