| Budget Amount *help |
¥19,630,000 (Direct Cost: ¥15,100,000、Indirect Cost: ¥4,530,000)
Fiscal Year 2015: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2014: ¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
Fiscal Year 2013: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2012: ¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
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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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