Moduli spaces in graded ring theory - Sue Sierra (Edinburgh) - Edinburgh Geometry Seminar
Date: Thursday 20th October.
Speaker: Sue Sierra (Edinburgh).
Title: Moduli spaces in graded ring theory
Abstract: Let R be a noetherian N-graded algebra, generated in degree 1,
over the complex numbers. A point module is a cyclic R-module with
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).
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.
We show that this geometry characterises naive blowup algebras. This is joint work with Tom Nevins.
Speaker: Sue Sierra (Edinburgh).
Title: Moduli spaces in graded ring theory
Abstract: Let R be a noetherian N-graded algebra, generated in degree 1,
over the complex numbers. A point module is a cyclic R-module with
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).
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.
We show that this geometry characterises naive blowup algebras. This is joint work with Tom Nevins.
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