Math 145 - Undergraduate Algebraic Geometry

This course provides an introduction to algebraic geometry. We will begin by studying affine varieties, projective spaces, projective varieties and maps between them. We will establish a dictionary between geometry and algebra; one of the important tools here will be Hilbert's Nullstellensatz. Next, we will look at plane curves. We will prove Bezout's theorem and show some of its applications. We will define the addition law on plane cubic curves - a more detailed discussion of elliptic curves will be given. The end of the course will present more advanced topics, such as the existence of 27 lines on the cubic surface.

Instructor: Dragos Oprea, oprea "at", Room 382D (2nd floor).

Lectures: MWF, 11am-11:50am.

Office hours: Th 2:15-4:15, 382D

Course Assistant:Yu-jong Tzeng, yjt "at", Room 380L

Office hours: M 3-5pm, TTh 10:30-12, W 4:10-5:10.

Textbook: Miles Reid - Undergraduate algebraic geometry.

Prerequisites: This course is intended for 3rd or 4th year undegraduate students. I expect that people taking the class will have some background in algebra at the level of Math 120. For instance, I will assume familiarity with fields, rings, polynomial rings etc. It will be useful to know some complex analysis at the level of 116. Familiarity with basic point-set topology may be beneficial but not required. Some knowledge of manifolds will be even better but definitely not required.

Exams: There will be a take-home midterm and a take-home final.

Problem Sets: There will be weekly problem sets, usually due on Friday in class. The problem sets will be posted online. Group work is encouraged, but you have to hand in your own write up of the homework problems.

Final Grades:

Important dates:

Tentative syllabus: PDF

Lecture Summaries


Homework 1 due Monday, April 14, in class PDF.

Homework 2 due Friday, April 18, in class PDF.

Homework 3 due Friday, April 25, in class PDF.

Homework 4 due Friday, May 2, in class PDF.

Midterm due Wednesday, May 7, in class PDF.

Homework 5 due Friday, May 16, in class PDF.

Homework 6 due Friday, May 23, in class PDF.

Homework 7 due Friday, May 30, in class PDF.

Final Exam due Friday, June 6 (or the latest on Monday June 9 at 11:30AM), in my mailbox PDF.