Quiver Grassmannians associated with string modules
G. Cerulli Irelli
Dipartimento di Matematica Pura ed Applicata, Università degli studi di Padova, Via Trieste 63, 35121 Padova, Italy
DOI: 10.1007/s10801-010-0244-6
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 [( A)\tilde] p,1 \tilde{A}_{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).
Pages: 259–276
Keywords: keywords cluster algebras; cluster character; quiver grassmannians; Euler characteristic; string modules
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References
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