论文标题
椭圆曲线的非交通同源镜对称性
Noncommutative homological mirror symmetry of elliptic curves
论文作者
论文摘要
通过Orlov的Landau-Ginzburg/Calabi-yau对应关系，我们证明了两个A-赋值函数的等效性。一个是椭圆曲线的polishchuk-zaslow的镜像对称函数，另一个是从2-torus的福卡亚类别到非交换矩阵因素化类别的局部镜像函数。作为推论，我们证明了非共同镜像函子实现了任何翻译参数$ t $的同源镜像对称性。
We prove an equivalence of two A-infinity functors, via Orlov's Landau-Ginzburg/Calabi-Yau correspondence. One is the Polishchuk-Zaslow's mirror symmetry functor of elliptic curves, and the other is a localized mirror functor from the Fukaya category of the 2-torus to a category of noncommutative matrix factorizations. As a corollary we prove that the noncommutative mirror functor realizes homological mirror symmetry for any translation parameter $t$.
