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Abstract:
The aim of this talk is to advertise quiver Grassmannians, a
family of projective algebraic varieties which are a
far-reaching generalization of ordinary Grassmannians. The
quiver Grassmannian associated to a quiver representation M and a
nonnegative integer vector e is the variety of subrepresentations of
M with the dimension vector e. The Euler characteristics of these
varieties have an unexpected application (due to Caldero, Chapoton and
Keller) to cluster algebras. We discuss some examples of quiver
Grassmannians and some of their general properties (sufficient
conditions for smoothness and for the positivity of the Euler
characteristic).
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