Although this uses wordpress technology, this is not a blog. The purpose of this site is to get advice and suggestions on continually evolving notes on the foundations of algebraic geometry.

These notes deal with schemes, and 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, after taking serious courses in commutative algebra, topology, complex analysis, differential geometry, homological algebra, and number theory.  We do not live in an ideal world.

I’ve officially taught this course at Stanford three times (and unofficially ran reading courses more often than that), and my lecture notes have been converging over time.  The notes distill things people have told me through the years, of slick explanations of the basic things one needs to know to work in algebraic geometry.  I would now like to refine them further, by digesting into it more collective wisdom.

My intent for the 2010-2011 academic year (September 2010 – August 2011) was to gradually and sequentially edit them, and to post them, roughly at the rate of a (hard, fast) course.  This goal is now complete. My intent for the 2011-2012 academic year is to teach a year-long graduate course at Stanford, and continue to post the notes, and continue to have interesting discussions with people via this site, which will lead to ongoing revision and improvements.

See these mathoverflow answers for some interesting discussion just before this started.