Math 216: Foundations of algebraic geometry 2005-06

The course webpage for the 2009-10 version of the course is here. You should go there first. The course webpage for the 2007-08 version of the course is here.

All notes in four big files

Here are the notes, as of June 28, 2007. You can check below to see which notes have been updated: they are in bold. Fall. Winter. Spring. Problem sets. Everything in one huge file.

These notes are quite rough, and roughly reflect what I did in class. A new version is available from the 2007-08 class page, and a better version accompanies the 2009-10 class, so this particular file (and all remaining errors) will stay frozen. Later corrections are below, in bold. I will eventually remove this webpage, as all material here is trumped by later pages.

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. This is not 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 a first approximation.

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.

References: The posted lecture notes are rough, so I recommend having another source you like, for example Mumford's Red Book of Varieties and Schemes (the original edition is better, as Springer introduced errors into the second edition by retyping it), and Hartshorne's Algebraic Geometry. Both books are on reserve at the library. Hartshorne should be available at the bookstore. For background on commutative algebra, I'd suggest consulting Eisenbud's Commutative Algebra with a view toward algebraic geometry or Atiyah and MacDonald's Commutative Algebra. For background on abstract nonsense, Weibel's Introduction to Homological Algebra is good to have handy. Justin Walker also points out that Freyd's Abelian Categories is available online (free and legally) here.

Homework: Unlike most advanced graduate courses, there will be homework. It is important --- this material is very dense, and the only way to understand it is to grapple with it at close range.

Notes: Notes for the classes in ps and pdf formats will be posted here. Caution: All of these notes are quite rough, and just approximate transcriptions of my lecture notes. I encourage you to take notes yourselves, and not just rely on these. However, if you feel like pointing out improvements, I would appreciate it, as these notes are crudely extracted from a larger set of notes that I hope to make available eventually. Note that I give the dates of the last important update.

Fall quarter

Winter quarter
Spring quarter

Many thanks to Justin Walker for improving the class notes immeasurably!

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