Course info for Math 632 (Algebraic Geometry II) is available here.

We will primarily be following Ravi Vakil's notes Foundations of Algebraic Geometry, beginning in Chapter 13.

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 (current schedule: M 11am-12pm, T 3pm-4pm, R 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).

Problem sets will be posted here every 1-2 weeks and should be submitted by e-mail (my address is in the course info link above) - please have the subject line be "632 - Problem Set N".

Problem Set 1 (due Thursday, February 4)

Problem Set 2 (due Tuesday, February 16)

Problem Set 3 (due Thursday, February 25)

Problem Set 4 (due Thursday, March 4)

Problem Set 5 (due Tuesday, March 16)

Problem Set 6 (due Thursday, March 25)

Problem Set 7 (due Thursday, April 8)

The final project is due on Tuesday, April 20; some info/notes about it (and some suggested topics) are here.

Upcoming rough schedule (will update each Thursday or Friday for the following week):

Jan 19-21: Introduction, locally free and quasicoherent sheaves (13.1-13.5)

Jan 26-28: Coherent sheaves, Geometric Nakayama's Lemma, effective Cartier divisors (13.6, 13.7, 14.3)

Feb 2-4: Weil divisors, class groups (14.2)

Feb 9-11: quasicoherent sheaves on projective schemes, line bundles as maps to projective space (15.1, 15.2, 15.4, 16.3, 16.4)

Feb 16-18: more with maps to projective space, very ample line bundles, projective morphisms (16.4, 15.3, 16.6, 17.1-17.3)

Feb 23-25: Cech cohomology (18.1-18.3)

Mar 2-4: Euler characteristic, genus, Riemann-Roch/Serre duality, Hilbert polynomials (18.4-18.6)

Mar 9-11: Curves, week 1 (19.1-19.3, 19.6-19.8)

Mar 16-18: Curves, week 2 (19.4-19.5, 19.9)

Mar 25: Elliptic curves are group schemes, intro to differentials (19.10, some of 21.1-21.2)

Mar 30-Apr 1: more differentials (21.2-21.4, a little of 21.5)

Apr 6-8: a little Hodge theory, unramified morphisms, Riemann-Hurwitz (21.5-21.7)

Apr 13-20: proving Riemann-Roch, roughly following the approach in Chapter 2 of "Algebraic Groups and Class Fields" by Serre, see also https://math.stanford.edu/~vakil/725/bagsrr.pdf

Lecture notes: 0119, 0121, 0126, 0128, 0202, 0204, 0209, 0211, 0216, 0218, 0223, 0225, 0302, 0304, 0309, 0311, 0316, 0318, 0325, 0330, 0401, 0406, 0408, 0413, 0415, 0420