论文标题
福卡亚（Landau-Ginzburg Orbifolds）类别
Fukaya category for Landau-Ginzburg orbifolds
论文作者
论文摘要
对于加权均匀的多项式和对角线对称组的选择，我们为Landau-Ginzburg Orbifold（Fano或Calabi-Yau型）定义了新的福卡亚类别。该结构基于其Milnor纤维的包裹福卡亚类别以及奇异性的单构型，它类似于奇异理论中的变异操作员。新的$ \ ai $结构是使用带有单片轨道内部插入的冰棒图构建的。这就需要冰棍模量空间的新紧凑型，其中某些球和圆盘的共形结构由于冰棒结构而被对齐。尤其是，Conimension One冰棒球可能存在，并成为定义$ \ ai $结构的障碍物。对于log fano和calabi-yau案例，我们表明球体气泡不是由动作和程度估计引起的，以及对Milnor纤维纤维商的扭曲Reeb轨道指数的计算。
For a weighted homogeneous polynomial and a choice of a diagonal symmetry group, we define a new Fukaya category for a Landau-Ginzburg orbifold (of Fano or Calabi-Yau type). The construction is based on the wrapped Fukaya category of its Milnor fiber together with the monodromy of the singularity, and it is analogous to the variation operator in singularity theory. The new $\AI$-structure is constructed using popsicle maps with interior insertions of the monodromy orbit. This requires new compactifications of popsicle moduli spaces where conformal structures of some of the spheres and discs are aligned due to the popsicle structures. In particular, codimension one popsicle sphere bubbles might exist and become obstructions to define the $\AI$-structure. For log Fano and Calabi-Yau cases, we show that the sphere bubbles do not arise from action and degree estimates, together with the computation of indices of twisted Reeb orbits for Milnor fiber quotients.
