EVENT DETAILS AND ABSTRACT

Title: Moduli spaces of points on some quantum varieties
Speaker: Tom Nevins
Speaker Info: UIUC
Brief Description:
Special Note:
Abstract:

The study of point modules over a graded noncommutative algebra R---an analog of skyscraper sheaves on a projective variety---has played a central role in classification results in noncommutative ring theory. If the algebra R is strongly noetherian (i.e. tensoring with any commutative noetherian algebra gives another noetherian algebra), connected graded, and generated in degree 1, then its point modules are parametrized by a projective scheme. By contrast, a strange new class of algebras, the naive blow-ups, exhibit a puzzling phenomenon: their point modules cannot be parametrized by any scheme locally of finite type. I'll explain the resolution of this puzzle. Namely, there are two parameter spaces, one of which is a fine moduli space but not a scheme, and the other of which is a projective variety but only a coarse moduli space. The two moduli spaces are related by an analog of the Hilbert-Chow morphism. This is joint work with Susan Sierra.