2012 Fiscal Year Final Research Report
STUDY ON DERIVED CATEGORIES AND STABILITY CONDITIONS
| Project/Area Number |
23740012
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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 |
Algebra
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| Research Institution | Oyama National College of Technology (2012)
Kyoto University (2011) |
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Principal Investigator |
OKADA So 小山工業高等専門学校, 一般科, 講師 (50547015)
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| Project Period (FY) |
2011 – 2012
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| Keywords | ホモロジカルミラー対称性、 / 導来圏、 / 安定性条件、 / 周期 |
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| Research Abstract |
We worked on derived categories and stability conditions, using homological mirror symmetries and wall-crossings. We studied the homological mirror symmetry of equivariant derived categories and with central charges of solutions of Picard-Fuchs equations [Hosono 04][Kontsevich 12], we constructed stability conditions of Bridgeland type for the Fermat Calabi-Yau threefold. We obtained wall-crossings by such solutions. Also, we obtained a clear asymptotic formula for Euler characteristics of moduli spaces of stable representations of m-Kronecker quivers.
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