Quiver Grassmannians associated with string modules

Abstract

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 "orientable string modules". As an application we explicitly compute the Euler-Poincaré characteristic of quiver Grassmannians associated with indecomposable pre-projective, pre-injective and regular homogeneous representations of an affine quiver of type Ãp,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). © 2010 Springer Science+Business Media, LLC.