曲线奇点的同调berglund - h bsch镜像对称

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Symplectic Geometry 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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来源期刊

Journal of Symplectic Geometry 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.