复曲面Calabi-Yau 3-褶皱镜上的拉格朗日截面
Lagrangian sections on mirrors of toric Calabi-Yau 3-folds
摘要：
本文构造了三维锥丛上Lagrange环面纤维化的Lagrange截面，它是镜像环面Calabi-Yau 3-fold上全纯线丛的SYZ对偶。然后，我们证明了一个环同构之间的包装Floer上同调的零截面和正则函数的镜像复曲面Calabi-Yau 3倍。进一步证明了当Calabi-Yau 3-fold是仿射空间时，零截面生成镜像锥丛的包裹范畴.这使我们能够完成证明的一个方向的同调镜像对称的复曲面卡-丘orbifold的形式$\mathbb{C}^3/\Check{G}$。我们完成描述我们的计算辛拓扑的一些基本应用。
英文摘要：
We construct Lagrangian sections of a Lagrangian torus fibration on a 3-dimensional conic bundle, which are SYZ dual to holomorphic line bundles over the mirror toric Calabi-Yau 3-fold. We then demonstrate a ring isomorphism between the wrapped Floer cohomology of the zero-section and the regular functions on the mirror toric Calabi-Yau 3-fold. Furthermore, we show that in the case when the Calabi-Yau 3-fold is affine space, the zero section generates the wrapped Fukaya category of the mirror conic bundle. This allows us to complete the proof of one direction of homological mirror symmetry for toric Calabi-Yau orbifold quotients of the form $\mathbb{C}^3/\Check{G}$. We finish by describing some elementary applications of our computations to symplectic topology.
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