Course info for Math 631 (Algebraic Geometry I) is available here.

The current office hours schedule is: M 10-11am in EH 3842, W 8-9pm on Zoom (details in link above), F 4-5pm in EH 3842.

The final office hours of the term will be on Mon Dec 9, but you are welcome to e-mail me if you want to schedule a meeting after then.

We will be loosely following Ravi Vakil's notes 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 Gradescope and announcements.

Weekly problem sets will be posted here on Thursday afternoons and will be due on the following Thursday. Submissions should be done on Gradescope (can access via Canvas).

Problem Set 1 (due Thursday, September 12)

Problem Set 2 (due Thursday, September 19)

Problem Set 3 (due Thursday, September 26)

Problem Set 4 (due Thursday, October 3)

Problem Set 5 (due Thursday, October 10)

Problem Set 6 (due Thursday, October 17)

Problem Set 7 (due Thursday, October 24)

Problem Set 8 (due Thursday, October 31)

Problem Set 9 (due Thursday, November 7)

Problem Set 10 (due Thursday, November 14)

Problem Set 11 (due Thursday, November 21)

Problem Set 12 (due Thursday, December 5)

Rough schedule (with section numbers from FoAG):

Aug 27-29: introduction to course, presheaves, sheaves, pushforwards (2.1-2.2)

Sep 3-5: stalks, categories of (pre)sheaves, sheafification, abelian categories (2.3-2.4, 2.6).

Sep 10-12: Spec A (as a set and topological space), functoriality (3.1-3.5)

Sep 17-19: topological properties of Spec A, the dictionary between ring theory and scheme theory, the structure sheaf (3.6-3.7, 4.1)

Sep 24-26: 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 1-3: A-schemes, A-valued points, reduced and non-reduced schemes, integral schemes (the rest of 7.3, some of 5.2)

Oct 8-10: more with integral schemes, projective space, Proj (5.2, 4.4.9, 4.5)

Oct 17: maps of projective schemes, the definition of closed embeddings (7.4, a little of 9.1)

Oct 22-24: Fiber products of schemes, fibers of morphisms (10.1-10.3)

Oct 29-31: closed embeddings, Bezout's theorem, the Veronese embedding, the Segre embedding (9.1, 9.3, 10.6)

Nov 5-7: assorted properties of schemes and morphisms (5.1, 5.3, 8.1-8.3)

Nov 12-14: separated morphisms, the category of k-varieties and rational maps, proper morphisms (11.1-11.4, 7.5.6)

Nov 19-21: dimension and codimension (12.1-12.4)

Nov 26: tangent spaces, regularity, curve singularities (13.1-13.3, 5.4)

Dec 3-5: the Jacobian criterion, Bertini's theorem, DVRs, Algebraic Hartogs's Lemma, definition of the class group (13.3-13.5, 15.4.10)