2017 Fiscal Year Final Research Report
Construction of Lagrangian fibrations
Project/Area Number 
26400032

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Multiyear Fund 
Section  一般 
Research Field 
Algebra

Research Institution  Hokkaido University 
Principal Investigator 

Project Period (FY) 
20140401 – 20180331

Keywords  シンプレクティック / ラグランジアン 
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.

Free Research Field 
高次元代数幾何学
