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 will cover affine and projective varieties corresponding roughly to the first chapter of Hartshorne.

The course description can be found here.

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

Lectures: MWF, 10:00-10:50, AP&M 7-421.

Office hours:

Wednesday 1-2:30pm in AP&M 6-101. The office hours will be hybrid, the zoom link can be found in Canvas

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

Textbook: I will roughly follow Andreas Gathamnn's notes available online. I recommend that you also consult Shafarevich's Basic Algebraic Geometry and Hartshorne's Algebraic Geometry.

Other useful texts 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. The problem sets are submitted via Gradescope.

Important dates:

Lecture Summaries


Homework 1 due Friday, Sept 30 - PDF

Homework 2 due Friday, October 7 - PDF

Homework 3 due Monday, October 17 - PDF

Homework 4 due Monday, October 24 - PDF

Homework 5 due Monday, October 31 - PDF

Homework 6 due Monday, November 7 - PDF

Homework 7 due Monday, November 14 - PDF

Homework 8 due Monday, November 21 - PDF

Homework 9 due Friday, December 2 - PDF