论文标题
富卡亚类别之间的函数的同源镜子对称性
Homological mirror symmetry for functors between Fukaya categories of very affine hypersurfaces
论文作者
论文摘要
我们证明，非常仿生的超曲面的同源镜子对称性尊重某些自然符号操作（作为部分包裹的福卡亚类别之间的函子），验证了AUROUX的猜想。这些猜想涉及镜子对称性的伴随性超表面及其补体之间的兼容性，这本身也是一个非常非常仿生的超表面。我们发现，呈现高呈阳性的互补实际上有两个天然镜子，其中之一是派生的方案。这两个镜子是通过Knörrer周期性介导的非几何等效性相关的。奥鲁克斯的猜想需要进行一些修改才能考虑到这一点。我们的证明还介绍了将liouville歧管作为liouville部门的新技术。
We prove that homological mirror symmetry for very affine hypersurfaces respects certain natural symplectic operations (as functors between partially wrapped Fukaya categories), verifying conjectures of Auroux. These conjectures concern compatibility between mirror symmetry for a very affine hypersurface and its complement, itself also a very affine hypersurface. We find that the complement of a very affine hypersurface has in fact two natural mirrors, one of which is a derived scheme. These two mirrors are related via a non-geometric equivalence mediated by Knörrer periodicity; Auroux's conjectures require some modification to take this into account. Our proof also introduces new techniques for presenting Liouville manifolds as gluings of Liouville sectors.
