| Budget Amount *help |
¥12,870,000 (Direct Cost: ¥9,900,000、Indirect Cost: ¥2,970,000)
Fiscal Year 2017: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2014: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
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| Outline of Final Research Achievements |
The Donaldson-Tian-Yau conjecture for anti-canonical polarization was recently solved affirmatively by Chen-Donaldson-Sun and Tian. However, this conjecture is still open for general polarizations or more generally in extremal Kaehler cases. We mainly worked in this unsolved cases of the conjecture.
For a polarized algebraic manifold, by introducing the concept of strong relative K-stability, we showed that strong relative K-stability implies asymptotic relative Chow stability. In particular, a strong relative K-stable polarized algebraic manifold always admits a sequence of polybalanced metric that are expected to converge to an extremal Kaehler metric in the polarization class. This then shows that the sequence of polybalanced metrics admits a suitable a priori bound. Moreover, we obtained a couple of results on the related problems.
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