Course info for Math 632 (Algebraic Geometry II) is available here, including the current office hours schedule (M 3-4pm, T 3-4pm, F 2-3pm, all in EH 3842).

Tuesday office hours this week (April 4) are rescheduled to Thursday, April 6, 4-5pm.

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.

Problem sets will be posted here every 1-2 weeks and should be submitted on Gradescope (linked on Canvas).

Problem Set 1 (due Thursday, January 19)

Problem Set 2 (due Thursday, February 2)

Problem Set 3 (due Thursday, February 9)

Problem Set 4 (due Thursday, February 16)

Problem Set 5 (due Thursday, February 23)

Problem Set 6 (due Tuesday, March 14)

Problem Set 7 (due Thursday, March 23)

Problem Set 8 (due Thursday, April 6)

The final project is due on Tuesday, April 18; some info/notes about it (and some suggested topics) are here.

Rough schedule (with section numbers from FoAG):

Jan 5: introduction, definition of a quasicoherent sheaf (6.1-6.2)

Jan 10-12: locally free sheaves and coherent sheaves, Geometric Nakayama's Lemma (6.4, 14.1-14.3)

Jan 17-19: effective Cartier divisors and Weil divisors (15.1-15.3)

Jan 24-26: principal and locally principal Weil divisors, computing Picard groups, pulling back divisors, quasicoherent sheaves on projective schemes (15.2, 17.3.9, 16.1)

Jan 31-Feb 2: quasicoherent sheaves on projective schemes, line bundles as maps to projective space (16.2-16.3, 17.4)

Feb 7-9: linear systems, globally generated sheaves, very ample line bundles, relative Spec and Proj (17.4, 17.6, 18.1-18.3)

Feb 14-16: Cech cohomology (19.1-19.3)

Feb 21-23: Euler characteristic, genus, Riemann-Roch, Hilbert polynomials (19.4-19.6)

March 7-9: Curves, week 1 (20.1-20.3, 20.6-20.8)

March 14-16: Curves, week 2 (20.4-20.5)

March 21-23: Curves, week 3 + differentials, week 1 (20.9-20.10, 22.1-22.2)

March 28-30: Differentials, week 2 (22.2, 22.4, some of 22.3 and 22.5)

April 4-6: a little Hodge theory, ramification, Riemann-Hurwitz (22.5-22.7)

April 11-18: 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