Math 206 - Points on surfaces

Instructor: Dragos Oprea, doprea "at", AP&M 6-101.

Lectures: WF, 1:30-2:50am, APM 7421.

Course description:

The topic for Math 206 this quarter is the Hilbert scheme of points on surfaces.

In the beginning of the course, we will construct the Hilbert scheme in full generality. This is important for a number of moduli problems in algebraic geometry.

For the Hilbert scheme of points on surfaces, we will compute some of the topological invariants. In particular, we express the Euler characteristics in terms of modular forms. Connections with the representation theory of affine Lie algebras will be made.

(This may be a bit too ambitious for a one quarter course, so the goals may change slightly as we go.)

Office hours: I am available for questions after lecture or by appointment. Also, feel free to drop in if you see me in my office.


I will make an attempt to be as self-contained as the topic permits. However, I will assume background in algebraic geometry at the level of Math 203.

The course is intended for graduate students in Mathematics, though everybody is welcome. There will be no homework or exams for this course if you are a math graduate student; the grade will be based entirely on attendance.


Lecture Summaries