2016 Fiscal Year Final Research Report
Study of noncommutative Hodge structures in mirror symmetry
| Project/Area Number |
26610008
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 代数学 / 幾何学 / 数理物理学 / ミラー対称性 |
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| Outline of Final Research Achievements |
Mirror symmetry is a symmetry which interchanges the role of the symplectic geometry and complex algebraic geometry. The purpose of this reserch is a trial for a deep understanding of the non-commutative Hodge theory in the theorey of the mirror symmetry and for a solution to important problems in related areas.
The following are examples of our research results. Motivated by the non-commutative Hodge theory for categories of matrix factorizations, we proposed a set of axioms for orbifold Jacobian algebras, and we proved the existence and the uniqueness of them. We have also been studying the entropy of endo-functors on derived categories of coherent sheaves on smooth projective varieties and show the Gromov-Yomdin type theorem for some varieties.
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| Free Research Field |
複素幾何学・数理物理学
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