论文标题
Toric del-pezzo表面的热带Lagrangians
Tropical Lagrangians in toric del-Pezzo surfaces
论文作者
论文摘要
我们查看一个人如何从二聚体模型的数据中构造lagrangian submanifold，in $（\ mathbb {c}^*）^n $其评估投影近似于热带超声表面。二聚体的每个面对应于我们热带拉格朗日submanifold上边界的拉格朗日磁盘，形成了拉格朗日突变种子。使用此功能，我们发现了热带拉格朗日摩tori $ l_ {t^2} $在平滑的反典型的Del-pezzo的平滑反典型分裂中，其墙壁变换与单调Syz纤维的变换相匹配。为镜子对$（\ mathbb {cp}^2 \ setminus e，w）制定了一个示例，\ check x_ {9111} $。我们发现$ \ mathbb {cp}^2 \ setMinus e $互换$ l_ {t^2} $和syz纤维的符号切除型。有证据表明，这种符号切除型是镜子的镜头，$ \ check x_ {9111} $。
We look at how one can construct from the data of a dimer model a Lagrangian submanifold in $(\mathbb{C}^*)^n$ whose valuation projection approximates a tropical hypersurface. Each face of the dimer corresponds to a Lagrangian disk with boundary on our tropical Lagrangian submanifold, forming a Lagrangian mutation seed. Using this we find tropical Lagrangian tori $L_{T^2}$ in the complement of a smooth anticanonical divisor of a toric del-Pezzo whose wall-crossing transformations match those of monotone SYZ fibers. An example is worked out for the mirror pair $(\mathbb{CP}^2\setminus E, W), \check X_{9111}$. We find a symplectomorphism of $\mathbb{CP}^2\setminus E$ interchanging $L_{T^2}$ and a SYZ fiber. Evidence is provided that this symplectomorphism is mirror to fiberwise Fourier-Mukai transform on $\check X_{9111}$.
