论文标题
$ a _ {\ infty} $ singularity的群集结构
Cluster structures for the $A_{\infty}$ singularity
论文作者
论文摘要
我们研究$ \ mathbb {z} $的类别$ \ mathcal {c} _2 $ of Mathbb {z} $ - 分级的MCM模块在$ a_ \ infty $ curve singularity上，并证明它具有无限型$ a $ a $ cluster compinatorics。特别是，我们表明该Frobenius类别（或合适的子类别）稳定等于Holm-Jorgensen，Fisher和Paquette-Yildirim的无限类型$ $ cluster类别。结果，$ \ Mathcal {c} _2 $具有群集倾斜子类别，该类别由（已完成的）$ \ infty $ -gon建立了某些三角形。我们使用Frobenius结构进一步扩展了这一点，以考虑最大的几乎刚性子类别，并表明这些子类别及其突变显示了已完成的$ \ infty $ -GON的组合。
We study a category $\mathcal{C}_2$ of $\mathbb{Z}$-graded MCM modules over the $A_\infty$ curve singularity and demonstrate it has infinite type $A$ cluster combinatorics. In particular, we show that this Frobenius category (or a suitable subcategory) is stably equivalent to the infinite type $A$ cluster categories of Holm-Jorgensen, Fisher and Paquette-Yildirim. As a consequence, $\mathcal{C}_2$ has cluster tilting subcategories modelled by certain triangulations of the (completed) $\infty$-gon. We use the Frobenius structure to extend this further to consider maximal almost rigid subcategories, and show that these subcategories and their mutations exhibit the combinatorics of the completed $\infty$-gon.
