We study quiver Grassmannians associated with indecomposable representations (of finite dimension) of the Kronecker quiver. We find a cellular decomposition for them and we compute their Betti numbers. As an application, we find a geometric realization for the atomic basis of cluster algebras of type affine-A1 found by Sherman and Zelevinsky (who called it the canonical basis) and those of type affine-A2 found in an earlier paper of the first author.
Geometry of quiver Grassmannians of Kronecker type and applications to cluster algebras / CERULLI IRELLI, Giovanni; Esposito, Francesco. - In: ALGEBRA & NUMBER THEORY. - ISSN 1937-0652. - 5:6(2011), pp. 777-801. [10.2140/ant.2011.5.777]
Geometry of quiver Grassmannians of Kronecker type and applications to cluster algebras
CERULLI IRELLI, GIOVANNI;
2011
Abstract
We study quiver Grassmannians associated with indecomposable representations (of finite dimension) of the Kronecker quiver. We find a cellular decomposition for them and we compute their Betti numbers. As an application, we find a geometric realization for the atomic basis of cluster algebras of type affine-A1 found by Sherman and Zelevinsky (who called it the canonical basis) and those of type affine-A2 found in an earlier paper of the first author.| File | Dimensione | Formato | |
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