There are several types of courses that can go under the name of “introduction to algebraic geometry”: complex geometry; the theory of varieties; a non-rigorous examples-based course; algebraic geometry for number theorists (perhaps focusing on elliptic curves); and more. There is a place for each of these courses. This course will deal with schemes, and will attempt to be faster and more complete and rigorous than most, but with enough examples and calculations to help develop intuition for the machinery. Such a course is normally a “second course” in algebraic geometry, and in an ideal world, people would learn this material over many years. We do not live in an ideal world. To make things worse, I am experimenting with the material, and trying to see if a non-traditional presentation will make it possible to help people learn this material better, so this year’s course is only an approximation. (See here for an earlier version.)
This course is for mathematicians intending to get near the boundary of current research, in algebraic geometry or a related part of mathematics. It is not intended for undergraduates or people in other fields; for that, people should take Brian Conrad’s undergraduate class in winter 2012, or else wait for a later incarnation of Math 216 (which will vary in style over the years).
In short, this not a course to take casually. But if you have the interest and time and energy, I will do my best to make this rewarding.