This is an introductory talk concerning quiver Grassmannians. A quiver Grassmannian is a projective variety which parametrizes the subrepresentations of a quiver representation which have a fixed dimension vector. If the quiver representation has good homological properties one can hope to study the geometry of the associated quiver Grassmannians by using the representation theory of quivers. The main open problem on this subject is if the quiver Grassmannians associated to a rigid quiver representation admit a cellular decomposition. I will report on recent developments on this problem. This is joint work with F. Esposito, H. Franzen and M. Reineke. |

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