Existence problem of canonical Kaehler metrics and GIT-stability
| Project/Area Number |
26800033
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 定スカラー曲率ケーラー計量 / 端的ケーラー計量 / 一般化されたケーラー・アインシュタイン計量 / 強K-安定性 / 相対K-安定性 / 相対Ding-安定性 / 一様相対K-安定性 / 一様相対Ding-安定性 / GIT安定性 / K-安定性 / Chow-安定性 / 一様K-安定性 |
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| Outline of Final Research Achievements |
Firstly, we clarified all the uniformly relatively Ding stable toric Fano manifolds whose dimensions are four or less. Next, we showed that the uniform relative K-stability for polarized toric manifolds implies the coercivity of the modified K-energy. Furthermore, we gave a sufficient condition for uniform relative K-stability by using the Delzant polytope corresponding polarized toric manifolds. For toric Fano manifolds, our sufficient condition is equivalent to the relative Ding-stability. In particular, we can see that the relative Ding-stability implies the uniform relative K-stability for toric Fano manifolds.
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Report
(5 results)
Research Products
(12 results)
