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 serve as preparation for a course in scheme theory (which may be covered in Math 203bc). Math 203bc will be taught by Professor Mark Gross in the Winter and Spring quarters.

We will study affine and projective algebraic varieties, and their properties. Among others, we will consider concepts such as smoothness, singularities, dimension, intersection multiplicities. I hope to illustrate the general theory with many examples. The goal is to cover roughly the first chapter (+epsilon) of Hartshorne's book.

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

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

Office hours:

W 3-4, Th 1-2, 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: Robin Hartshorne - Algebraic geometry.


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 10.
  • Withdrawal deadline: October 24.
  • Veterans Day: November 11.
  • Thanksgiving break: November 27-28.
  • Last day of classes: December 5.

Tentative syllabus: PDF

Lecture Summaries

Notes: There may be typos in the files below, let me know if you spot any serious ones.
Additional resources:

Homework 1 due Monday Oct 6 PDF.

Homework 2 due Monday Oct 13 PDF.

Homework 3 due Monday Oct 20 PDF.

Homework 4 due Monday Oct 27 PDF.

Homework 5 due Monday Nov 10 PDF.

Homework 6 due Monday Nov 17 PDF.

Homework 7 due Monday Nov 24 PDF.

Homework 8 due Friday Dec 5 PDF.