A famous result of Zimmermann-Huisgen, Hille and Reineke asserts that any projective variety occurs as a quiver Grassmannian for a suitable representation of some wild acyclic quiver. We show that… Expand

We provide a technique to compute the Euler–Poincaré characteristic of a class of projective varieties called quiver Grassmannians. This technique applies to quiver Grassmannians associated with… Expand

Torus fixed points of quiver moduli spaces are given by stable representations of the universal (abelian) covering quiver. As far as the Kronecker quiver is concerned they can be described by stable… Expand

We study quiver Grassmannians associated with indecomposable representations of the Kronecker quiver. We find a cellular decomposition of them and we compute their Betti numbers. As an application,… Expand

We provide a technique to compute the Euler---Poincare characteristic of a class of projective varieties called quiver Grassmannians. This technique applies to quiver Grassmannians associated with… Expand

Recent articles have shown the connection between representation theory of quivers and the theory of cluster algebras. In this article, we prove that some cluster algebras of type ADE can be… Expand

We show that the cohomology ring of a quiver Grassmannian asssociated with a rigid quiver representation has property (S): there is no odd cohomology and the cycle map is an isomorphism; moreover,… Expand