The study of ideal limits of sequences of test configurations
| Project/Area Number |
25610012
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Osaka University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
二木 昭人 東京大学, 大学院数理科学研究科, 教授 (90143247)
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| Co-Investigator(Renkei-kenkyūsha) |
NAKAGAWA Yasuhiro 佐賀大学, 大学院工学研究科, 教授 (90250662)
NITTA Yasufumi 東京工業大学, 大学院理工学研究科, 助教 (90581596)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | テスト配位列 / K-安定性 / Donaldson-二木不変量 / polybalanced計量 / 相対安定性 / 偏極代数多様体 |
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| Outline of Final Research Achievements |
We made a systematic study of the completion of the moduli space of test configurations for a polarized algebraic mamifold. As a typical example of our study, we obtain the Donaldson-Futaki invariant for sequences of test configurations on a polarized algebraic manifold. This then allows us to introduce the concept of strong K-stability. Moreover, by a joint work with Nitta, we showed that strong K-stability implies asymptotic Chow stability. These results in particular give us various applications in the existence problem of extremal Kaehler metrics.
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Report
(5 results)
Research Products
(13 results)
