曲线奇点的同调Berglund-Hübsch镜像对称
辛几何
2020-03-13 v3 代数几何
摘要
给定一个二元可逆多项式,我们证明其最大分次矩阵因子化范畴拟等价于其Berglund-Hübsch转置的Fukaya-Seidel范畴。此前Futaki-Ueda对Brieskorn-Pham和型奇点证明了该结论。证明涉及在B侧显式构造倾斜对象,并与A侧一组特定的Lefschetz薄层基进行比较。
引用
@article{arxiv.1903.01351,
title = {Homological Berglund-H\"ubsch mirror symmetry for curve singularities},
author = {Matthew Habermann and Jack Smith},
journal= {arXiv preprint arXiv:1903.01351},
year = {2020}
}
备注
34 pages, 17 figures. Comments welcome. v2 Minor updates. v3 Incorporates referee comments. To appear in Journal of Symplectic Geometry