Homological Berglund-Hübsch mirror symmetry for curve singularities

曲线奇点的同调 Berglund-Hübsch-Henningson 镜像对称

Homological Berglund-Hübsch-Henningson mirror symmetry for curve singularities

本文证明曲线奇点的同调 Berglund-Hübsch-Henningson 镜像对称，通过拉回超势实现等变性，并证明矩阵分解范畴存在倾斜对象，长度等于 FJRW 状态空间维数。

Berglund-Hübsch Milnor纤维的镜像对称性

Mirror symmetry for Berglund-Hübsch Milnor fibers

该研究通过先计算甚仿射Fukaya范畴再进行形变的方法，计算Berglund-Hübsch可逆多项式的Milnor纤维的Fukaya范畴，大体证明了相关同调镜像对称猜想，核心是确定反常schober的典范延拓。

On homological mirror symmetry for chain type polynomials

We consider Takahashi's categorical interpretation of the Berglund-Hubsch mirror symmetry conjecture for invertible polynomials in the case of chain polynomials. Our strategy is based on a stronger claim that the relevant categories satisfy a recursion of directed $A_{\infty}$-categories, which may be of independent interest. We give a full proof of this claim on the B-side. On the A-side we give a detailed sketch of an argument, which falls short of a full proof because of certain missing foundational results in Fukaya-Seidel categories, most notably a generation statement.

Seifert form of chain type invertible singularities

In this paper, we confirm a conjecture of Orlik-Randell from 1977 on the Seifert form of chain type invertible singularities. We use Lefschetz bifibration techniques as developed by Seidel (inspired by Arnold and Donaldson) and take advantage of the symmetries at hand. We believe that our method will be useful in understanding the homological/categorical version of Berglundt-Hubsch mirror conjecture for invertible singularities.