论文标题
SYZ镜面对称性，用于Del Pezzo表面和仿射结构
SYZ mirror symmetry for del Pezzo surfaces and affine structures
论文作者
论文摘要
我们证明，Del Pezzo表面的Landau-Ginzburg超电势可以被实现为其Hyperkähler旋转向大型复杂结构限制点的极限。作为推论，我们计算由collins-jacob--lin构建的特殊拉格朗日纤维的复杂仿射结构的极限ARXIV：2205.07753。我们还使用cho-hong-hong-hong-lau arxiv：1810.02045和hong-kim-kim-kim-lau arxiv：1805.11738的粘合方法，构建了$ a_n $ singularities $ a_n $ singularities and Monotone del pezzo表面平滑的平滑镜和单调的平滑镜子。他们同意Hyperkähler旋转的结果。
We prove that the Landau--Ginzburg superpotential of del Pezzo surfaces can be realized as a limit of their hyperKähler rotation toward the large complex structure limit point. As a corollary, we compute the limit of the complex affine structure of the special Lagrangian fibrations constructed by Collins--Jacob--Lin in $\mathbf{P}^1\times \mathbf{P}^1$ arXiv:1904.08363 and compare it with the integral affine structures used in the work of Carl--Pumperla--Siebert arXiv:2205.07753. We also construct the Floer-theoretical Landau--Ginzburg mirrors of smoothing of $A_n$-singularities and monotone del Pezzo surfaces, by using the gluing method of Cho--Hong--Lau arXiv:1810.02045 and Hong--Kim--Lau arXiv:1805.11738. They agree with the result of hyperKähler rotation.
