2017 Fiscal Year Final Research Report
Construction of Lagrangian fibrations
| Project/Area Number |
26400032
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Hokkaido University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | シンプレクティック / ラグランジアン |
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| Outline of Final Research Achievements |
We investigated the linear system associated to ample divisors and an automorphism group of an irreducible symplectic manifold using deformation of complex structure. Regarding the former, we obtain the following
result. Let X be the set of the complex structures which defining the mapping and Y the set of the complex structures which defining the embedding in the projective space. Both X and Y are open in the space of deformation of the complex structures of irreducible symplectic manifolds. With respect to the latter, by appropriately deforming the complex structure, we prove that an automorphism group of irreducible symplectic manifold contain an infinite cyclic group whose rank equals to the second Betti number minus two.
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| Free Research Field |
高次元代数幾何学
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