论文标题
同源性Berglund-Hübsch-Henningson镜面对称曲线奇点
Homological Berglund-Hübsch-Henningson mirror symmetry for curve singularities
论文作者
论文摘要
在本文中，我们为曲线奇异性建立了同源性berglund-hübsch镜子对称性，其中A-模型融合了均衡性（也称为同源性Berglund-Hübsch--Henningson Mirror对称性），包括某些类别的变形。更确切地说，我们在Arxiv：1004.0078中证明了Futaki和UEDA的猜想，它认为可以通过向相应的可鸡蛋分辨率的总空间拉回a-Model中的均衡性。在此过程中，我们表明矩阵分解的B-模型类别具有倾斜对象，其长度是FJRW A-模型的状态空间的维度，这一结果可能具有独立的兴趣，因为它在Landau-Ginzburg dubrovin的猜测中的含义。
In this article, we establish homological Berglund--Hübsch mirror symmetry for curve singularities where the A--model incorporates equivariance, otherwise known as homological Berglund--Hübsch--Henningson mirror symmetry, including for certain deformations of categories. More precisely, we prove a conjecture of Futaki and Ueda in arXiv:1004.0078 which posits that the equivariance in the A-model can be incorporated by pulling back the superpotential to the total space of the corresponding crepant resolution. Along the way, we show that the B--model category of matrix factorisations has a tilting object whose length is the dimension of the state space of the FJRW A--model, a result which might be of independent interest for its implications in the Landau--Ginzburg analogue of Dubrovin's conjecture.
