Complex analysis and stability of a polarized manifold
| 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 |
|
|---|
| Project Period (FY) |
2015-08-28 – 2017-03-31
|
| Project Status |
Completed (Fiscal Year 2016)
|
| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
|---|
| 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 / K安定性 / 自己同型群 |
|---|
| 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.
|
Report
(3 results)
Research Products
(10 results)
