The Geometry of Points on Quantum Projectivizations

Suppose S is an affine, noetherian scheme, X is a separated, noetherian S-scheme, is a coherent X-bimodule, and T( ) is a graded ideal. We study the geometry of the functor Γn of flat families of truncated = T( )/ -point modules of length n + 1. We then use the results of our study to show that if Proj is a quantum ruled surface, the point modules over are parameterized by the closed points of X2( ). When X = 1, we construct, for any -point module, a graded X − -bimodule resolution.