本项目是代数表示论和代数几何的交叉课题。我们拟刻画丛倾斜代数（特别是 gentle 丛倾斜代数）的 Cohen-Macaulay Auslander 代数的结构和表示论基本性质，特别是刻画 rigid 模的性质。在此基础上，我们将利用丛倾斜代数的 Cohen-Macaulay Auslander 代数的 quiver Grassmannian 实现丛倾斜代数的 quiver Grassmannian 的奇点消解。

This proposal is about the intersection of representation theory of algebras and algebraic geometry. We will describe the structure of the Cohen-Macaulay Auslander algebras of the (gentle) cluster-tilted algebras, and also study their properties related to representation theory, especially their rigid modules. Furthermore, we will study the quiver Grassmannians of the cluster-tilted algebras, namely, use the quiver Grassmannians of the Cohen-Macaulay Auslander algebras of the cluster-tilted algebras to realize the desingularization of the quiver Grassmannians of the cluster-tilted algebras, especially the Gorenstein projective modules.