2010 Fiscal Year Final Research Report
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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| Keywords | 微分幾何 / シンプレクティック幾何 |
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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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