Quiver Grassmannians associated with string modules

Abstract

We provide a technique to compute the Euler characteristic of a class of projective varieties called quiver Grassmannians. This technique applies to quiver Grassmannians associated with "orientable string modules". As an application we explicitly compute the Euler characteristic of quiver Grassmannians associated with indecomposable preprojective, preinjective and regular homogeneous representations of an affine quiver of type ${\tilde{A}}_{p,1}$. For $p=1$, this approach provides another proof of a result due to P. Caldero and A. Zelevinsky in \cite{CZ}.

Minor changes. Accepted at the Journal Of Algebraic Combinatorics

References in corpus (6)

• Quiver varieties and cluster algebras
• Quiver Varieties and Branching
• Positivity for cluster algebras from surfaces
• Quivers with potentials and their representations II: Applications to cluster algebras
• From triangulated categories to cluster algebras
• Geometry of quiver Grassmannians of Kronecker type and canonical basis of cluster algebras

Cited by in corpus (13)

• Quiver Grassmannians and degenerate flag varieties
• Geometry of quiver Grassmannians of Kronecker type and canonical basis of cluster algebras
• Generic Modules for string algebras
• Schubert decompositions for quiver Grassmannians of tree modules
• Euler characteristic of quiver Grassmannians and Ringel-Hall algebras of string algebras
• Representation type via Euler characteristics and singularities of quiver Grassmannians
• Toda Systems, Cluster Characters, and Spectral Networks
• Coefficient Quivers, ${\mathbb{F}}_1$-Representations, and Euler Characteristics of Quiver Grassmannians
• Desingularizations of Quiver Grassmannians for the Equioriented Cycle Quiver
• On Generalized Minors and Quiver Representations
• Scalar extensions of quiver representations over ${\mathbb{F}}_1$
• A multiplication formula for cluster characters in gentle algebras
• Equivariant cohomology of juggling varieties in rank one