C^\infty-logarithmic transformations and generalized complex structures
C^\infty-logarithmic transformations and generalized complex structures
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C^infty 对数变换和广义复数结构
DOI：
10.4310/jsg.2016.v14.n2.a1
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Kenta Hayano
中科院分区：
文献类型：
--
作者：
R. Goto;Kenta Hayano
利用沿2-环面的对数变换，构造了一个广义复结构J＿n，该结构对每个$n\geq 0$具有n型变化luci的1-Lefschetz属纤维，其中包括具有非零欧拉特征的椭圆曲面。在具有平凡法向束的辛2环面上，通过多重数为0的对数变换，得到了由辛流形得到的流形上具有任意大量变型座连通分量的扭曲广义复结构。$m\geq 0$、$(2n-1)\C P^2# (10n-1)\ol{\C P^2}$和$S^1\times S^3$的连通和$(2m+1)S^2\times S^2$允许具有任意大n的n型变化luci的扭曲广义复杂结构J＿n。
Applying logarithmic transformations along 2-tori, we construct a generalized complex structure J_n with n type changing luci for every $n\geq 0$ on genus 1-Lefschetz fibrations with a cusp neighborhood, which include elliptic surfaces with non-zero euler characteristic. Applying a technique of broken Lefschetz fibrations, we further obtain twisted generalized complex structures with arbitrary large numbers of connected components of type changing loci on the manifold which is obtained from a symplectic manifold by logarithmic transformations of multiplicity 0 on a symplectic 2-torus with trivial normal bundle. The connected sums $(2m+1)S^2\times S^2$ for $m\geq 0$, $(2n-1)\C P^2# (10n-1)\ol{\C P^2}$ and $S^1\times S^3$ admit twisted generalized complex structures J_n with n type changing luci for arbitrary large n.
影响因子：
2.5
作者：
R. Goto
通讯作者：
R. Goto