Mirror symmetry and brane tiling
| Project/Area Number |
20740037
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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 | Osaka University |
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Principal Investigator |
UEDA Kazushi 大阪大学, 大学院・理学研究科, 准教授 (60432465)
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| Project Period (FY) |
2008 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | ミラー対称性 / 例外列 / トーリック退化 / 安定導来圏 / 複素多様体 / シンプレクティック多様体 / ダイマー模型 / ホモロジー的ミラー対称性 / トーリックスタック / 導来圏 / コアメーバ / 旗多様体 / 完全可積分系 / ポテンシャル関数 |
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| Research Abstract |
With any two-dimensional toric weak Fano stack, we could associate a combinatorial object called a brane tiling, which allows us to describe the derived category of coherent sheaves on this stack in terms of representations of quivers. We have also proved homological mirror conjecture for a basic class of singularities called Brieskorn-Pham singularities. In a slightly different direction, we have computed the potential function for the torus fiber of the Gelfand-Cetlin system on flag varieties of type A.
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Report
(6 results)
Research Products
(38 results)
