Course info for Math 631 (Algebraic Geometry I) is available here, including the current office hours schedule (M 12-1pm in EH 3842, W 8-9pm on Zoom (details in link above), F 2-3pm in EH 3842).

I won't have my usual scheduled office hours on Wednesday, November 23, Friday, November 25, or Monday, November 28. Please e-mail me if you'd like to meet on Nov 23 or Nov 29/30 on the following week, or if you have any questions that can be answered by e-mail.

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 may set up a Canvas site for some logistical things, but the main course website will be here.

Weekly problem sets will be posted here on Thursday afternoons and will be due on the following Thursday before class by e-mail (you should e-mail it to the grader and cc me on the e-mail - our addresses are in the course info link above) - please have the subject line be "631 - Problem Set N".

Problem Set 1 (due Thursday, September 15)

Problem Set 2 (due Thursday, September 22)

Problem Set 3 (due Thursday, September 29)

Problem Set 4 (due Thursday, October 6)

Problem Set 5 (due Thursday, October 13)

Problem Set 6 (due Thursday, October 20)

Problem Set 7 (due Thursday, October 27)

Problem Set 8 (due Thursday, November 3)

Problem Set 9 (due Thursday, November 10)

Problem Set 10 (due Thursday, November 17)

Problem Set 11 (due Thursday, December 1)

Problem Set 12 (due Thursday, December 8)

Rough schedule (with section numbers from FoAG - Note: a new version of FoAG was posted on Sep 2, so references are now to that version.):

Aug 30-Sep 1: introduction to course, presheaves, sheaves, pushforwards (2.1-2.2)

Sep 6-8: stalks, categories of (pre)sheaves, sheafification, abelian categories (2.3-2.4, 2.6)

Sep 13-15: Spec A (as a set and topological space), functoriality (3.1-3.5)

Sep 20-22: topological properties of Spec A, the dictionary between ring theory and scheme theory, the structure sheaf (3.6-3.7, 4.1)

Sep 27-29: schemes, locally ringed spaces, non-affine schemes, projective space, morphisms of schemes (4.3-4.4, 7.1-7.2, some of 7.3)

Oct 4-6: A-schemes, k-valued points, properties of schemes and morphisms (the rest of 7.3, 5.1-5.2, some of 8.3)

Oct 11-13: non-reduced schemes, more properties of schemes and morphisms, affine-local properties (5.2-5.3, normality from 5.4, more of 8.3)

Oct 20: affine morphisms (8.3)

Oct 25-27: the Lying Over theorem, closed embeddings, back to Proj (part of 8.2, 9.1, part of 4.5)

Nov 1-3: projective schemes, maps of projective schemes, Bezout's theorem, the Veronese embedding (4.5, 7.4, 9.3)

Nov 8-10: fiber products of schemes (10.1-10.4)

Nov 15-17: the Segre embedding, separated morphisms (10.6, 11.1-11.4)

Nov 22: the category of k-varieties and rational maps, proper morphisms (7.5.6, 11.5)

Nov 29, Dec 1: dimension, (co)tangent spaces, regularity/smoothness (12.1-12.4, 13.1-13.3)

Dec 6, Dec 8: discrete valuation rings, introduction to line bundles, sketches of theorems about curves (13.5, various topics from chapters 14-18)