Math 259B - Enumerative Geometry and Moduli Theory

Welcome to Math 259!

Course description:

The basic question of enumerative geometry can be simply stated as:

How many geometric objects of a given type satisfy given geometric conditions?

For instance, one may ask for

In many cases, this comes down to calculating intersection numbers on moduli spaces.

In the first part of the course, we will discuss Chern classes and show some of their applications to enumerative questions.

In the second part, I will give an introduction to the moduli space of curves. In particular, I hope to include a discussion of the Quot scheme, of geometric invariant theory, outline the construction of the moduli space, and possibly calculate one or two concrete intersection numbers.

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

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

Lectures: MWF, 12pm-12:50pm, TBA.

Office hours:

Wednesday 1-2pm.

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 a solid background in algebraic topology, and in algebraic geometry at the level of Math 203, or alternatively some background in complex geometry at the level of Math 250C.

There will be no homeworks or exams for this class.

Lecture Summaries