Note: this is the website for the Fall 2020 version of the class. For the Fall 2022 website, go here.

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

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

This class will be fully online. Lectures will happen via Zoom at the scheduled time for this class (TR 11:30am-1pm), and I will have virtual office hours (currently M 11am-12pm, W 2:30pm-3:30pm, F 4pm-5pm) on Zoom as well. Lecture recordings will be available for when people are unable to join the lectures at the scheduled time for some reason.

I will be using the Canvas website for this class (link) for virtual logistics (links to Zoom sessions, announcements). The page that you are currently reading will continue to be the home for math-related content (syllabus, links to references, problem sets, etc).

Weekly problem sets will be posted here on Thursday afternoons and will be due on the following Thursday by e-mail (my address is in the course info link above) - please have the subject line be "631 - Problem Set N".

Problem Set 1 (ungraded)

Problem Set 2 (due Thursday, September 24)

Problem Set 3 (due Thursday, October 1)

Problem Set 4 (due Thursday, October 8)

Problem Set 5 (due Thursday, October 15)

Problem Set 6 (due Thursday, October 22)

Problem Set 7 (due Thursday, October 29)

Problem Set 8 (due Thursday, November 5)

Problem Set 9 (due Thursday, November 12)

Problem Set 10 (due Thursday, November 19)

Problem Set 11 (due Tuesday, December 8)

Oct 20-22: more with affine morphisms (7.3.5-7.3.11), closed embeddings (8.1)

Oct 27-29: Projective schemes (4.5, 6.4, 8.2)

Nov 3-5: Veronese embeddings (8.2.6), scheme-theoretic image and induced reduced subscheme structure (8.3), fiber products of schemes (9.1, 9.2)

Nov 10-12: more with fiber products (9.3, 9.4), Segre embeddings (9.6), separated morphisms (10.1), rational maps (6.5, 10.2)

Nov 17-19: a little more with rational maps (6.5.7), proper morphisms (10.3), dimension (11.1-11.4)

Dec 1: the Zariski (co)tangent space (12.1), regularity/smoothness (12.2, 12.3, 12.5)

Dec 3: introduction to line bundles (topics from chapters 13-14)

Dec 8: theorems about curves (sketches of results from chapters 16-17)

Lecture notes: 0901, 0903, 0908, 0910, 0915, 0917, 0922, 0924, 0929, 1001, 1006, 1008, 1013, 1015, 1020, 1022, 1027, 1029, 1103, 1105, 1110, 1112, 1117, 1119, 1201, 1203, 1208