Blowing-up noncommutative weighted projective spaces (joint work with Colin Ingalls.)
For any positive integer n, the weighted projective space P(1,1,n) is defined to be Proj k[x,y,z], where x and y have degree 1 and z has degree n. This space has exactly one singular point, and if we blowup at this point, we get the smooth rational surface Fn. In this talk, we discuss the noncommutative analog of this construction. Starting with a noncommutative P(1,1,n), as defined by Stephenson, we will describe the process of blowing-up the ``singular point'' of the noncommutative weighted projective space. The resulting algebra, which resembles the homogeneous coordinate ring of a bundle of rational curves over a rational curve, is the homogeneous coordinate ring of a noncommutative analog of Fn . As time permits, we will describe the relationship between the blowing-up construction and the construction of noncommutative ruled surfaces using bimodules.