本项目是代数表示论和代数几何的交叉课题。我们拟研究2-CY-倾斜代数，有限维Jacobian代数，CM-有限代数，Cohen-Macaulay Auslander代数（CMA-代数），quiver Grassmannian的奇点消解等方面的问题。具体为：.(1）有限维Jacobian代数变换与2-CY-倾斜代数变换之间的关系，2-CY-倾斜代数变换保持CM-有限性的条件，tame型2-CY-倾斜代数的CM-有限性。.(2）刻画skewed-gentle 2-CY-倾斜代数的CMA-代数在导出等价、表示类型、Hall多项式等方面的性质。利用自入射代数的稳定范畴研究加权射影线丛倾斜代数的奇异范畴以及CM-有限性。.(3）实现skewed-gentle 2-CY-倾斜代数以及CM-有限型代数Cohen-Macaulay模quiver Grassmannian的奇点消解。

This proposal is about the intersection of representation theory of algebras and algebraic geometry. It concerns 2-CY-tilted algebras, finite-dimensional Jacobian algebras, CM-finiteness, Cohen-Macaulay Auslander algebras, quiver Grassmannians and their desingularization. More precisely,.(1).The relation between the mutation of the finite-dimensional Jacobian algebras and that of the 2-CY-tilted algebras, describe the condition for the mutation of the 2-CY-tilted algebras to preserve CM-finiteness, the CM-finiteness of the tame 2-CY-tilted algebras..(2).Describe the properties of the Cohen-Macaulay Auslander algebras of the skewed-gentle 2-CY-tilted algebras, such as derived equivalence classification, representation type and the existence of Hall polynomials. Use the stable categories of some selfinjective Nakayama algebras to describe the stable categories of the Cohen-Macaulay modules over the cluster-tilted algebras of the canonical algebras..(3).Realize the desingularization of the quiver Grassmannians of the skewed-gentle 2-CY-tilted algebras and the CM-finite algebras.