| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
The famous Yau-Tian-Donaldson conjecture states that the existence of standard Kahler metric is equivalent to the stability condition which is originated from Mumford's Geometric Invariant Theory. If there does not exist such a standard metric, we want to study a variety degenerating it to the stable one. We gave a new formulation to this problem, introduced a new geometric flow, and showed the existence of the long-time solution. Using this solution we further gave an asymptotic construction of the optimal degeneration.
We also provided some ideas to prove the existence of the standard metric when the automorphism group is possibly not finite.
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