Quiver Grassmannians associated with string modules

Details Quiver Grassmannians associated with string modules Quiver Grassmannians associated with string modules

2009-10-14

arxiv.org/abs/0910.2592v2

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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