曲线奇点的同调berglund - h bsch镜像对称

Pub Date : 2019-03-04 DOI:10.4310/JSG.2020.V18.N6.A2

Matthew Habermann, Jack Smith

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引用次数: 18

摘要

给定一个两变量可逆多项式，证明了它的最大分级矩阵分解的范畴拟等价于它的Berglund-Hubsch转置的fukya - seidel范畴。这是Futaki-Ueda之前对Brieskorn-Pham和$D$型奇点的证明。证明包括在b面明确构造一个倾斜的物体，并与a面Lefschetz顶针的特定基础进行比较。

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Homological Berglund-Hübsch mirror symmetry for curve singularities

Given a two-variable invertible polynomial, we show that its category of maximally-graded matrix factorisations is quasi-equivalent to the Fukaya-Seidel category of its Berglund-Hubsch transpose. This was previously shown for Brieskorn-Pham and $D$-type singularities by Futaki-Ueda. The proof involves explicit construction of a tilting object on the B-side, and comparison with a specific basis of Lefschetz thimbles on the A-side.

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