Grassmannians and Cluster Algebras

This paper follows the program of study initiated by S. Fomin and A. Zelevinsky, and demonstrates that the homogeneous coordinate ring of the Grassmannian G ( k , n ) is a cluster algebra of geometric type . Those Grassmannians that are of finite cluster type are identified and their cluster variables are interpreted geometrically in terms of configurations of points in C P 2 . 2000 Mathematics Subject Classification 22E46, 05Exx.