We show that there are generalized complex structures on all 4-manifolds obtained by logarithmic transformations with arbitrary multiplicity along symplectic tori with trivial normal bundle. Applying a technique of broken Lefschetz fibrations, we obtain generalized complex structures with arbitrary large numbers of connected components of type changing loci on every manifold which is obtained from a symplectic 4-manifold by a logarithmic transformation of multiplicity 0 along a symplectic torus with trivial normal bundle. Elliptic surfaces with non-zero euler characteristic and the connected sums (Formula Presented) and S1 × S3 admit twisted generalized complex structures Jn with n type changing loci for arbitrary large n.
|ジャーナル||Journal of Symplectic Geometry|
|出版ステータス||Published - 2016|
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