2015 Fiscal Year Final Research Report
Study of Mirror Symmetry of Singularities
| Project/Area Number |
24684005
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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| Allocation Type | Partial Multi-year Fund |
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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) |
2012-04-01 – 2016-03-31
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| Keywords | 幾何学 / 代数学 / 数理物理学 / ミラー対称性 |
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| Outline of Final Research Achievements |
Based on the idea of Mirror Symmetry which interchanges the role of algebra and geometry, three kinds of flat structures (Frobenius structures) are associated to algebra, representation theory and geometry. For cusp singularities, we show the classical mirror symmetry, an isomorphism of the flat structure for algebra and geometry. We also show, by period mappings of the primitive form, an isomorphism of the flat structures for algebra and representation theory. Moreover, together with Homological Mirror Symmetry, the Dubrovin's conjecture holds for orbifold projective lines associated to rational polyhedral groups.
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| Free Research Field |
数学
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