## EVENT DETAILS AND ABSTRACT

**Geometry/Physics Seminar**
**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.

**Date:** Thursday, April 7, 2011

**Time:** 4:00pm

**Where:** Lunt 107

**Contact Person:** Jesse Wolfson

**Contact email:** wolfson@math.northwestern.edu

**Contact Phone:**

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