K-stability, degeneration of algebraic varieties
| Project/Area Number |
26870316
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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
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
Odaka Yuji 京都大学, 理学研究科, 准教授 (30700356)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | モジュライ空間 / 安定性 / 標準Kahler計量 / トロピカル幾何 / モジュライ / Fallings高さ / K-energy / Arakelov幾何 / K安定性 / 双有理幾何学 / ファノ多様体 / 反標準因子 / トロピカル幾何学 / ミラー対称性 / 非アルキメデス幾何 / Donaldson-二木不変量 / Kahler-Einstein計量 |
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| Outline of Final Research Achievements |
I improved the understanding of stability and moduli of algebraic varieties or arithmetic varieties. I constructed compact algebraic space of KE Fano smoothable varieties. I generalized so-called Faltings height to general arithmetic varieties as modular heights, and then established the basic of arithmetic or Arakelov theoretic aspect of the K-stability and canonical Kahler metrics. I also introduced what I call tropical geometric compactifications of moduli spaces and studied the structure in details. It is closely related to geometric aspect of Mirror symmetry (after Strominger-Yau-Zaslow), tropical geometry and non-archimedean geometry.
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Report
(4 results)
Research Products
(16 results)
