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

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

2010-03-15

arxiv.org/abs/1003.3037v2

Mathematics

Representation Theory

21 pages

Scientific paper

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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