| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
In this research, we achieved the following two results.
(1) For a given toric Fano manifold, we introduced an invariant of a Fano polytope which is likely to be a polar dual of the barycenter of the image under the moment map on a given toric Fano manifold. Under some assumption, it induces a simpler criterion for the existence of Kahler-Einstein metrics (or K stability) on a toric Fano manifold.
(2) With a differential geometrical approach, we extended the moment map interpretation for balanced metrics to relative balanced metrics. Then, it implies the quantization of the extremal metrics and the extremal vector fields on a polarized manifold.
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