| Project/Area Number |
21840017
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
GALKIN Sergey The University of Tokyo, 数物連携宇宙研究機構, 特任研究員 (10554503)
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| Project Period (FY) |
2009 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 幾何学 / トポロジー / 代数学 |
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| Research Abstract |
We had great outreach in media this year and also new exciting results : we constructed mirrors for all 105 families of smooth Fano threefolds, for 104 of these families we give a nice representation as toric complete intersection or its "unabelianization", thus we compute their genus zero Gromov-Witten invariants, and so we prove hypothesis of mirror symmetry (in what concerns differential equations) for these 104 families, we introduce a new but very fundamental notion of extremal local systems - those are acyclic and it is equivalent to minimization of some functional, we support our conjecture that all local systems associated with odd-dimensional Fano varieties via mirror symmetry are extremal by case of 104 families of smooth Fano threefolds. Our method doesn't depend on dimension and now machines in Imperial College are working out half billion four-dimensional candidates (computing the basic invariants will take approximately 2-3 more months).
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