2009 Fiscal Year Final Research Report
Stability conditions on Calabi-Yau 3-folds
| Project/Area Number |
20840006
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| Research Category |
Grant-in-Aid for Young Scientists (Start-up)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
TODA Yukinobu The University of Tokyo, 数物連携宇宙研究機構, 特任准教授 (20503882)
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| Project Period (FY) |
2008 – 2009
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| Keywords | Calabi-Yau 3-fold / Derived category / Stability condition / Donaldson-Thomas invariant |
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| Research Abstract |
Calabi-Yau 3-folds are important geometric objects in describing our universe, and they are important in both physics and mathematics. I studied the notion called `stability conditions' on them . This notion was introduced by Douglas, Bridgeland, but so far it has been difficult to construct stability conditions on Calabi-Yau 3-folds. So I proposed the weaker notion weak stability conditions' and in fact I succeeded in constructing them. Moreover I applied this notion to curve counting problem, and solved a certain conjecture (Pandharipande-Thomas conjecture).
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