论文标题
log calabi-yau表面的镜像对称性ii
Mirror Symmetry for log Calabi-Yau Surfaces II
论文作者
论文摘要
我们表明，具有最大边界的每个光滑仿射对数Calabi-yau表面的常规函数环具有通过其整数热带点和一个$ \ mathbb {C} $ - 代数结构的矢量空间基础，具有由keel-yu的几何结构给出的结构系数。为了证明这一结果，我们首先给出了与一对$（y，d）$相关的镜像家族的典型压实，其中由毛keel-keel构建，其中$ y $是一个平稳的投射理性表面，$ d $是一种反态的理性曲线循环，$ y \ y \ y \ y \ setminus d $是与aftine act and affine表面的最小值。然后，我们使用Ruddat-Siebert的技术来计算压缩家庭的时期，并使用它来对压缩镜家族进行模块化解释。
We show that the ring of regular functions of every smooth affine log Calabi-Yau surface with maximal boundary has a vector space basis parametrized by its set of integer tropical points and a $\mathbb{C}$-algebra structure with structure coefficients given by the geometric construction of Keel-Yu. To prove this result, we first give a canonical compactification of the mirror family associated with a pair $(Y,D)$ constructed by Gross-Hacking-Keel where $Y$ is a smooth projective rational surface, $D$ is an anti-canonical cycle of rational curves and $Y\setminus D$ is the minimal resolution of an affine surface with, at worst, du Val singularities. Then, we compute periods for the compactified family using techniques from work of Ruddat-Siebert and use this to give a modular interpretation of the compactified mirror family.
