Algebraic Geometry Seminar
Tom Nevins
UIUC
Moduli spaces of points on some quantum varieties
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.
Thursday November 11, 2010 at 4:00 PM in SEO 636