The syllabus for Math 631 (Algebraic Geometry I) is available here.

The office hours schedule for the first week is: Wed 2pm-3pm and Thu 2pm-4pm in EH 3842. I will post a survey on Canvas asking about good times for office hours for future weeks.

We will be loosely following Ravi Vakil's book Foundations of Algebraic Geometry.

As the semester progresses, I will post problem sets and a rough schedule of topics here. I've set up a basic Canvas site just for announcements.

Weekly problem sets will be posted here on Thursday afternoons. They will not count towards your grade in the course but you are still expected to think about them to follow along with the course material! Even though the problem sets will not count towards your grade, I highly encourage you to write down solutions to some or all of them and send them to me by e-mail (address in the linked syllabus above) for feedback. I am also happy to answer questions about specific problems by e-mail or in office hours.

Problem Set 0 will be posted on Thursday, September 3.

Rough schedule (with section numbers from FoAG):

Sep 1-3: introduction to course, presheaves, sheaves, pushforwards, stalks (2.1-2.2)

Sep 8-10: categories of (pre)sheaves, sheafification, abelian categories (2.3-2.4, 2.6).

Sep 15-17: Spec A (as a set and topological space), functoriality (3.1-3.5)

Sep 22-24: topological properties of Spec A, the dictionary between ring theory and scheme theory, the structure sheaf (3.6-3.7, 4.1)

Sep 29-Oct 1: schemes, locally ringed spaces, non-affine schemes, the projective line, morphisms of schemes (4.3-4.4, 7.1-7.2, some of 7.3)

Oct 6-8: A-schemes, A-valued points, reduced and non-reduced schemes, integral schemes (the rest of 7.3, some of 5.2)

Oct 13-15: more with integral schemes, projective space, Proj (5.2, 4.4.9, 4.5)

Oct 22: maps of projective schemes, the definition of closed embeddings (7.4, a little of 9.1)

Oct 27-29: Fiber products of schemes, fibers of morphisms (10.1-10.3)

Nov 3-5: closed embeddings, Bezout's theorem, the Veronese embedding, the Segre embedding (9.1, 9.3, 10.6)

Nov 10-12: assorted properties of schemes and morphisms (5.1, 5.3, 8.1-8.3)

Nov 17-19: in-class exam (Nov 19), separated morphisms, the category of k-varieties and rational maps (11.1-11.3, 7.5.6)

Nov 24: proper morphisms (11.4)

Dec 1-3: dimension and codimension, tangent spaces, regularity, curve singularities (12.1-12.4, 13.1-13.3, 5.4)

Dec 8-10: the Jacobian criterion, Bertini's theorem, DVRs, Algebraic Hartogs's Lemma, definition of the class group (13.3-13.5, 15.4.10)