18.725: Introduction to Algebraic Geometry

Update: click here for a much later version (really, a distant descendant)

The description in the course guide: "Introduces the basic notions and techniques of modern algebraic geometry. Algebraic sets, Hilbert's Nullstellensatz and varieties over algebraically closed fields. We relate varieties over the complex numbers to complex analytic manifolds. For varieties of dimension one (i.e. curves) we discuss the genus, divisors, linear series, line bundles and the Riemann-Roch theorem." Johan de Jong will be teaching the follow-up course in the spring. The class is in 24-407.

Here are various notes in dvi, ps, and pdf formats. (If you would like tar archives, just let me know; due to limited diskspace, I had to remove them from this page.) I've added all the corrections I've found (or been told about) on Dec. 30, 1999, so they are in as final form as they'll ever be. Here are other links:
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Ravi Vakil
Department of Mathematics Rm. 2-271
Massachusetts Institute of Technology
77 Massachusetts Ave.
Cambridge MA USA 02139
Phone: 617-253-2683 (but e-mail is better)
Fax: 617-253-4358
Email: vakil@math.mit.edu