Quiver Grassmannians associated with string modules

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 orientable string modules. As an application we explicitly compute the Euler-Poincare characteristic of quiver Grassmannians associated with indecomposable pre-projective, pre-injective and regular homogeneous representations of an affine quiver of type (A) over tilde (p, 1). For p = 1, this approach provides another proof of a result due to Caldero and Zelevinsky (in Mosc. Math. J. 6(3):411-429, 2006).