Date: Thursday 20th October.<br />Speaker: Sue Sierra (Edinburgh).<br />Title: Moduli spaces in graded ring theory<br /><br />Abstract: Let R be a noetherian N-graded algebra, generated in degree 1,<br />over the complex numbers. A point module is a cyclic R-module with<br />Hilbert series 1/(1-s). If R is strongly noetherian --- that is, it remains noetherian upon base extension --- then its point modules are parameterized by a projective scheme X, and this induces a canonical map from R to a twisted homogeneous coordinate ring on X. This technique was crucial in the analysis of noncommutative P^2's (regular algebras of dimension 3).<br />We study a non-strongly noetherian case: the noncommutative Rees rings known as naive blowup algebras. We show there is a stack that represents point modules, and that a certain equivalence relation on point modules is corepresented by a projective scheme.<br />We show that this geometry characterises naive blowup algebras. This is joint work with Tom Nevins.
