论文标题
开放的FJRW理论和镜子对称性
Open FJRW Theory and Mirror Symmetry
论文作者
论文摘要
我们为Landau-Ginzburg（LG）模型$（\ Mathbb {C}^2，μ_r\ timesμ_s，x^r+y^s）构建一个开放的枚举理论。不变性被定义为在模量空间上与后代的多个捆绑包的积分，该空间是一个带有拐角的真实的甲型。反过来，这些开放不变的生成函数会产生镜面LG模型，并具有平坦的坐标的多种变形。在建立开放的拓扑递归结果后，我们证明了与所有后代的尺寸为二维的LG/LG开放式镜对称定理。我们定义的开放不变剂并不是唯一的，而是取决于边界条件，这些条件在变化时会显示出不变的墙壁横断现象。我们描述了一个LG壁交叉组，将可能发生的墙壁交叉转换分类。
We construct an open enumerative theory for the Landau-Ginzburg (LG) model $(\mathbb{C}^2, μ_r\times μ_s, x^r+y^s)$. The invariants are defined as integrals of multisections of a Witten bundle with descendents over a moduli space that is a real orbifold with corners. In turn, a generating function for these open invariants yields the mirror LG model and a versal deformation of it with flat coordinates. After establishing an open topological recursion result, we prove an LG/LG open mirror symmetry theorem in dimension two with all descendents. The open invariants we define are not unique but depend on boundary conditions that, when altered, exhibit wall-crossing phenomena for the invariants. We describe an LG wall-crossing group classifying the wall-crossing transformations that can occur.
