Geometry of quiver Grassmannians of Dynkin type with applications to cluster algebras

被引：0

作者：

Irelli, Giovanni Cerulli ^{[1
]}

机构：

[1] Sapienza Univ Roma, Dipartimento Matemat G Castelnuovo, Piazzale Aldo Moro 5, I-00185 Rome, Italy

来源：

REPRESENTATION THEORY - CURRENT TRENDS AND PERSPECTIVES | 2017年

关键词：

Quiver Grassmannians; Dynkin quivers; cluster algebras; DIFFERENTIABLE STRUCTURES; COMPLETE-INTERSECTIONS; REPRESENTATIONS; DEGENERATIONS; POTENTIALS; MODULES; VARIETIES;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper includes a new proof of the fact that quiver Grassmannians associated with rigid representations of Dynkin quivers do not have cohomology in odd degrees. Moreover, it is shown that they do not have torsion in homology. A new proof of the Caldero Chapoton formula is provided. As a consequence a new proof of the positivity of cluster monomials in the acyclic clusters associated with Dynkin quivers is obtained. The methods used here are based on joint works with Markus Reineke and Evgeny Feigin.

引用

页码：13 / 45

页数：33

共 45 条

[1] DEGENERATIONS FOR THE REPRESENTATIONS OF AN EQUIORIENTED QUIVER OF TYPE-DM [J].