Mathematics – Combinatorics
Scientific paper
2009-10-14
Mathematics
Combinatorics
Minor changes. Accepted at the Journal Of Algebraic Combinatorics
Scientific paper
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}.
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