In this class, you will be introduced to some of the central ideas in algebraic geometry. Because the field is a synthesis of ideas from many different parts of mathematics, it usually requires a lot of background and experience. My intent is to try to aim this class at people with a strong background in algebra and a willingness to develop geometric intuition, but to also have it accessible to those who have taken Math 120 and are willing to work hard and learn new things on the fly.
I want to get across some of the main ideas while doing lots of calculations. As far as possible, I want the class to be able to understand proofs completely, while also seeing enjoyable consequences. This means that the course will have "episodes" of different topics, and I will change plans on the fly as it becomes clear what the audience needs in terms of background.
Instructor: Ravi Vakil (vakil@math, office 383-Q, office hours Tuesdays 3-5 pm).
Course Assistant: Donghai Pan (pandh@math,
(office 381-A, office hours Thursdays 3-5 pm, Friday 10-11 am).
Prerequisites: Comfort with rings and modules. At the very least, a strong background from Math 120. Background in commutative algebra, number theory, complex analysis (in particular Riemann surfaces), differential geometry, and algebraic topology will help. But I realize that many people in the class will have seen none of these things.
Please be sure you are on the course email list (by asking me). You needn't be officially enrolled in the class to be on the email list.
References: There will be no textbook for the course, but there are a number of good references. Examples: Miles Reid's "Undergraduate Algebraic Geometry", Bill Fulton's "Algebraic Curves" (freely and legally available here), Frances Kirwan's "Complex Algebraic Curves", Brendan Hassett's "Introduction to Algebraic Geometry", Cox-Little-O'Shea's "Ideals Varieties and Algorithms", ... A number of these books (Reid, Kirwan, and Cox-Little-O'Shea) are freely electronically available through the library (to those at Stanford).