Geometry of Ricci-flat manifolds and moment maps
| Project/Area Number |
19540067
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | The University of Tokyo |
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Principal Investigator |
KONNO Hiroshi The University of Tokyo, 大学院・数理科学研究科, 准教授 (20254138)
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| Project Period (FY) |
2007 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 微分幾何 / シンプレクティック幾何 / シンプレクティック多様体 / 幾何学的量子化 / ハイパーケーラー多様体 / モーメント写像 / ハイパーケーラー商 / 微分幾何学 / シンプレクティック幾何学 |
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| Research Abstract |
We studied the topology of hyperkahler quotients by tori. We showed that we can take the norm square of the hyperkahler moment map as a Morse function under certain conditions. As a result we derived a formula for the Betti numbers and, under certain conditions, determined the cohomology ring. We also studied geometric quantization of flag manifolds. We constructed the one parameter family of Kahler polarization starting from the standard one and converging to the real polarization coming from the Gelfand-Cetlin integrable system at quantum level.
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Report
(6 results)
Research Products
(22 results)
