Course description: This course provides an introduction to algebraic geometry. Algebraic geometry is a central subject in modern mathematics, and an active area of research. It has connections with number theory, differential geometry, symplectic geometry, mathematical physics, string theory, representation theory, combinatorics and others.
Math 203 is a three-quarter sequence. Math 203A covered affine and projective varieties. Math 203B focused more heavily on sheaves, schemes, and the modern language of algebraic geometry; Math 203C will be a continuation of this discussion. Topics to be covered: properties of morphisms of schemes (separated, proper, smooth, etale); projective morphisms (including blowups); the relationship between complex analytic and algebraic geometry (including Serre's GAGA theorem); Hilbert schemes; geometry of algebraic surfaces. (For some idea of my plans, see my past course web sites.)
Instructor: Kiran Kedlaya, kedlaya [at] math [etcetera], APM 7202.
Lectures: MWF 10-11, APM 7421.
Office hours: Wednesday 1-2. Appointments can also be made by email.
Textbook: No required text. I will provide my own notes. It may be helpful to have access to a copy of Hartshorne, Algebraic Geometry but UCSD students can get it as a legal free e-book download using SpringerLink. You may also find helpful Ravi Vakil's Math 216 lecture notes.
The ultimate technical reference for the theory of schemes is
Grothendieck's EGA Johan de Jong's Stacks Project. Do not try to read it cover to cover! Instead, feel free to search through
it for individual topics (including homework problems).
Prerequisites: Math 203B, preferably taken last quarter. If you do not meet this prerequisite, please contact me as soon as possible!
Grading: 100% homework (no final exam). Problem sets will be assigned weekly (see below); please do them! It is effectively impossible to learn this subject passively. Some flexibility with due dates is available as long as you ask before the original deadline. Collaboration and outside research is permitted; just declare it in as much detail as possible.
Calendar of lecture topics: