| Project/Area Number |
19740034
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
|
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| Research Institution | Tohoku University |
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Principal Investigator |
NISHINOU Takeo Tohoku University, 大学院・理学研究科, 助教 (50420394)
|
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| Project Period (FY) |
2007 – 2009
|
| Project Status |
Completed (Fiscal Year 2009)
|
| Budget Amount *help |
¥2,720,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥420,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥900,000 (Direct Cost: ¥900,000)
|
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| Keywords | 正則曲線 / ミラー対称性 / 複素多様体 / トロピカル幾何 / トーリック多様体 / 旗多様体 / フレアーホモロジー |
|---|
| Research Abstract |
The purpose of our study is, to reveal symmetries and structures which are ingeniously hidden in seemingly complicated geometric objects. We mainly developed two devises: One is the degeneration of manifolds, which decomposes complex objects into simpler parts, and the other is the mirror symmetry, which is a kind of duality transformation between geometric objects. As a result, we could define several invariants of manifolds, and calculate them.
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