Course info for Math 631 (Algebraic Geometry I) is available here, including the current office hours schedule (M 4-5pm in EH 3842, W 8-9pm on Zoom (details in link above), F 1-2pm in EH 3842).

There will be no office hours on Friday, December 1. My last scheduled office hour will be on Friday, December 8. As always, you are welcome to contact me to arrange a meeting outside of these hours.

We will be 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 14)

Problem Set 2 (due Thursday, September 21)

Problem Set 3 (due Thursday, September 28)

Problem Set 4 (due Thursday, October 5)

Problem Set 5 (due Thursday, October 12)

Problem Set 6 (due Thursday, October 19)

Problem Set 7 (due Thursday, October 26)

Problem Set 8 (due Thursday, November 2)

Problem Set 9 (due Thursday, November 9)

Problem Set 10 (due Thursday, November 16)

Problem Set 11 (due Thursday, November 30)

Problem Set 12 (due Wednesday, December 6)

Rough schedule (with section numbers from FoAG):

Aug 29-31: introduction to course, presheaves, sheaves, pushforwards (2.1-2.2)

Sep 5-7: stalks, categories of (pre)sheaves, sheafification, abelian categories (2.3-2.4, 2.6). Here are the notes from Zoom; you can also e-mail me for links to recordings.

Sep 12-14: Spec A (as a set and topological space), functoriality (3.1-3.5)

Sep 19-21: topological properties of Spec A, the dictionary between ring theory and scheme theory, the structure sheaf (3.6-3.7, 4.1)

Sep 26-28: 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 3-5: A-schemes, k-valued points, properties of schemes and morphisms (the rest of 7.3, 5.1, 5.3, some of 8.3)

Oct 10-12: reduced and non-reduced schemes, normality, affine morphisms (5.2, normality from 5.4, more of 8.3)

Oct 19: finite and integral morphisms, the Lying Over theorem (8.2-8.3)

Oct 24-26: closed embeddings, projective space, Bezout's Theorem (9.1, 4.4.9, 9.4)

Oct 31-Nov 2: images of morphisms, Proj, projective schemes, maps of projective schemes, Bezout's theorem (8.4, 4.5, 7.4, 9.3)

Nov 7-9: the Veronese embedding, fiber products of schemes (9.3, 10.1-10.4)

Nov 14-16: the Segre embedding, separated morphisms (10.6, 11.1-11.4)

Nov 21: the category of k-varieties and rational maps, proper morphisms (7.5.6, 11.5)

Nov 28-30: dimension, (co)tangent spaces, regularity/smoothness (12.1-12.4, 13.1-13.3)

Dec 5: Bertini's theorem, DVRs (13.4-13.5)