Homological Mirror Symmetry of Isolated Hypersurface Singularities With Group Actions
| Project/Area Number |
20684003
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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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 |
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| Project Period (FY) |
2008 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
|
| Budget Amount *help |
¥16,900,000 (Direct Cost: ¥13,000,000、Indirect Cost: ¥3,900,000)
Fiscal Year 2011: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2010: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2009: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2008: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
|
|---|
| Keywords | 幾何学 / 代数学 / 数理物理学 / ミラー対称性 / 特異点 |
|---|
| Research Abstract |
Based on the idea of the Mirror symmetry which interchanges the role of the algebra and the geometry, three kinds of triangulated categories are associated to the algebra, the representation theory and the geometry. Looking at some properties of these triangulated categories, we show that the" Arnold' s strange duality" is now naturally understood as a mirror symmetry between orbifold curves and cusp singularities with group action, which is generalized to an infinite series of singularities.
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Report
(6 results)
Research Products
(74 results)
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[Book] ミラー対称性入門2009
Author(s)
江口徹, 深谷賢治, 高橋篤史, 並河良典, 細野忍, 今野宏, マーティンゲスト, 藤隆史, 中島啓
Publisher
日本評論社
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