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arXiv · 1003.3037

Geometry of quiver Grassmannians of Kronecker type and canonical basis of cluster algebras

Giovanni Cerulli Irelli·Francesco Esposito
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Abstract

We study quiver Grassmannians associated with indecomposable representations of the Kronecker quiver. We find a cellular decomposition of them and we compute their Betti numbers. As an application, we give a geometric realization of the "canonical basis" of cluster algebras of Kronecker type (found by Sherman and Zelevinsky) and of type $A_2^{(1)}$.

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BibTeXRIS

Giovanni Cerulli Irelli, Francesco Esposito. 2010-03-22. Geometry of quiver Grassmannians of Kronecker type and canonical basis of cluster algebras. https://doi.org/10.2140/ant.2011.5.777

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