标题： 一种用于类型$\widetilde{D}_n$的非$τ$-刚性模的几何模型 显示英文标题

标题： A geometric model for the non-$τ$-rigid modules of type $\widetilde{D}_n$

摘要： 我们为无$\tau$-刚性模在无向路径代数类型$\widetilde{D}_n$上提供了一个几何模型。 类似的模型也已为类型$A_n, D_n,$和$\widetilde{A}_n$的路径代数上的模范畴以及类型$\widetilde{D}_n$的$\tau$-刚性模提供过。 这些几何模型的一个主要优点是它们通常带有“交点-维数公式”。 这些公式将表示模的曲线的交点数与两个模之间的扩张空间的维数相等。 这个公式允许我们通过组合方法计算两个模之间的同调数据。 由于类型$\widetilde{D}_n$的 Auslander-Reiten 量子图的正则部分中存在无限多个不同的同质稳定管，且所有管都是不相交的，因此我们的几何数据需要在几何模型中的可接受边上有额外的装饰，以防止来自 Auslander-Reiten 量子图的不同稳定管中的模对应的曲线之间发生交集。 显示英文摘要

摘要： We give a geometric model for the non-$\tau$-rigid modules over acyclic path algebras of type $\widetilde{D}_n$. Similar models have been provided for module categories over path algebras of types $A_n, D_n,$ and $\widetilde{A}_n$ as well as the $\tau$-rigid modules of type $\widetilde{D}_n$. A major draw of these geometric models is the "intersection-dimension formulas" they often come with. These formulas give an equality between the intersection number of the curves representing the modules in the geometric model and the dimension of the extension spaces between the two modules. This formula allows us to calculate the homological data between two modules combinatorially. Since there are infinitely many distinct homogeneous stable tubes in the regular component of the Auslander-Reiten quiver of type $\widetilde{D}_n$, all of which are disjoint, our geometric data requires an extra decoration on the admissible edges in our geometric model to prevent intersections between curves corresponding to modules in distinct stable tubes of the Auslander-Reiten quiver.