Math 203A - Algebraic Geometry

Welcome to Math 203a!

Course description:

This course provides an introduction to algebraic geometry. Algebraic geometry is a central subject in modern mathematics, and an active area of research. It has connections with number theory, differential geometry, symplectic geometry, mathematical physics, string theory, representation theory, combinatorics and others.

Math 203 is a three quarter sequence. Math 203a (Fall Quarter) will be cover affine and projective varieties (roughtly the first 2/3 of the quarter) and basics of scheme theory (the last 1/3 of the quarter).

The course description can be found here .

Kiran Kedlaya will teach Math 203b and Math 203c in the Winter and Spring.

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

Lectures: WF, 11-12:20, AP&M 7-421.

Office hours:

Wednesday 1-2 PM in AP&M 6-101.

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

Textbook: There is no required textbook. I will follow Andreas Gathamnn's notes available online .

Other useful texts are

More advanced but useful references are:

Additional resources:


Some knowledge of modern algebra at the level of Math 200 is required. I will try to keep the algebraic prerequisites to a minimum. Familiarity with basic point set topology, complex analysis and/or differentiable manifolds is helpful to get some intuition for the concepts. Since it is hard to determine the precise background needed for this course, I will be happy to discuss prerequisites on an individual basis. If you are unsure, please don't hesitate to contact me.

There will be no exams for this class. The grade will be based entirely on homeworks and regular attendance of lectures. The problem sets are mandatory and are a very important part of the course.

Important dates:

  • First Class: September 28.
  • Veterans Day: November 12.
  • Thanksgiving break: November 22-23.
  • Last day of classes: December 7.


Lecture Summaries


Homework 1 due Friday, Oct 5 PDF

Homework 2 due Monday, Oct 15 PDF

Homework 3 due Wednesday, Oct 24 PDF

Homework 4 due Friday, November 2 PDF

Homework 5 due Friday, November 9 PDF

Homework 6 due Monday, November 19 PDF

Homework 7 due Wednesday, November 28 PDF

Homework 8 due Friday, December 7 PDF