2012 Fiscal Year Final Research Report
On Lagrangian fibratins of symplectic varieties
| Project/Area Number |
21684001
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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| Allocation Type | Single-year Grants |
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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) |
2009 – 2012
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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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| Research Abstract |
We show that the base space of a Lagrangian fibration is a projective space if the source symplectic variety satisfies certain numerical conditions. We obtain the necessary and sufficient condition of existence of a Lagrangian fibration for all known examples. We also show smoothness of components of the relative moduli space of aLagrangian fibration which parametrize invertible sheaves on each fibre.
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