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 two 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 Winter Quarter will cover more scheme theory, sheaf cohomology, algebraic curves, Riemann-Roch, Serre duality.

The course description can be found here .

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

Lectures: MW, 2pm-3:20pm, AP&M 7-421 (will most likely change).

Office hours:

Tuesday 2-4 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:

Notes: There may be typos in the files below, let me know if you spot any serious ones.
  • Complete notes from a course taught in Spring 2008, courtesy of David Philipson PDF.
  • Notes on resultants PDF.
  • Notes on irreducibility and dimension PDF.
Additional resources:


Some knowledge of modern algebra at the level of Math 200 is required. However, I will not assume background in commutative algebra. Familiarity with complex analysis, basic point set topology, differentiable manifolds is helpful, but not required. 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. The problem sets will be posted online.

Important dates:

  • Drop deadline: October 9.
  • Withdrawal deadline: October 23.
  • Veterans Day: November 11.
  • Thanksgiving break: November 26-27.
  • Last day of classes: December 4.

Lecture Summaries