论文标题
正常交叉表面，下降和镜子对称性的奇异性类别
Singularity categories of normal crossings surfaces, descent, and mirror symmetry
论文作者
论文摘要
给定一个平稳的3倍$ y $，一个线条捆绑$ l \ to y $，以及$ l $的$ s $ s $ $ s $ l $，使得$ s $的消失基因座是一个普通的杂交表面$ x $，带有类似图形的奇异基因座，我们提出了一种重建$ x $的$ x $类别的$ x $类别的$ x $ $ x $ $ x $ $ xyzizz fixrix factorizizz fix.xyz faceizizz fix.xyz的方法： \ mathbb {a}^{3} \ to \ mathbb {a}^{1} $（镜像到这双裤子的福卡亚类别）。这扩展了我们先前的结果，即$ L $被琐碎的情况。关键技术是矩阵因数化类别的非两性周期自动等同的分类。我们还根据拉比诺维茨（Rabinowitz）包裹了fukaya fukaya类别的ganatra-gao-venkatesh，为某些符合性的四个manifolds展示了这些奇异性类别的猜想镜，并将这种构造与lekili-ueda和jeffs的工作联系起来。
Given a smooth 3-fold $Y$, a line bundle $L \to Y$, and a section $s$ of $L$ such that the vanishing locus of $s$ is a normal crossings surface $X$ with graph-like singular locus, we present a way to reconstruct the singularity category of $X$ as a homotopy limit of several copies of the category of matrix factorizations of $xyz : \mathbb{A}^{3} \to \mathbb{A}^{1}$ (the mirror to the Fukaya category of the pair of pants). This extends our previous result for the case where $L$ is trivialized. The key technique is the classification of non-two-periodic autoequivalences of the category of matrix factorizations. We also present a conjectural mirror for these singularity categories in terms of the Rabinowitz wrapped Fukaya categories of Ganatra-Gao-Venkatesh for certain symplectic four-manifolds, and relate this construction to work of Lekili-Ueda and Jeffs.
