C∞-logarithmic transformations and generalized complex structures
C∞-logarithmic transformations and generalized complex structures
复制标题
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
R. Goto;Kenta Hayano
中科院分区：
文献类型：
--
作者：
R. Goto;Kenta Hayano
我们证明了在沿沿着具有平凡法丛的辛环面的任意重对数变换所得到的所有4个流形上都存在广义复结构。应用断裂Lefschetz纤维化的技巧，得到了在辛4-流形上通过沿着具有平凡法丛的辛环面的重数为0的对数变换得到的每个流形上具有任意大量变型轨迹连通分支的广义复结构.对于任意大的n，具有非零椭圆特征的椭圆曲面和连通和（2 m − 1）S × S，（2 m − 1）CP #lCP 2和S × S都存在具有n型变化轨迹的扭曲广义复结构Jn.
We show that there are generalized complex structures on all 4manifolds 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 (2m− 1)S × S, (2m− 1)CP #lCP 2 and S × S admit twisted generalized complex structures Jn with n type changing loci for arbitrary large n.