The syllabus for Math 632 (Algebraic Geometry II) is available here.

The current office hours schedule is: Mon/Wed 1pm-2pm, Thu 2pm-3pm, all in EH 3842. If you'd like to meet at some other time, just send me an e-mail.

We will be loosely 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 announcements.

Weekly problem sets will be posted here on Thursday afternoons. They will not count towards your grade in the course but you are still expected to think about them to follow along with the course material! Even though the problem sets will not count towards your grade, I highly encourage you to write down solutions to some or all of them and send them to me by e-mail (address in the linked syllabus above) for feedback. I am also happy to answer questions about specific problems by e-mail or in office hours.

Problem Set 1 (posted Thursday, January 15)

Problem Set 2 (posted Thursday, January 22)

Problem Set 3 (posted Thursday, January 29)

Problem Set 4 (posted Thursday, February 5)

Problem Set 5 (posted Thursday, February 12)

Problem Set 6 (posted Thursday, February 19)

Problem Set 7 (posted Thursday, February 26)

Problem Set 8 (posted Thursday, March 12)

Problem Set 9 (posted Thursday, March 19)

Problem Set 10 (posted Thursday, April 2)

The final project/oral exam must be completed by Tuesday, April 21; some info/notes about it (and some suggested topics) are here.

Rough schedule (with section numbers from FoAG):

Jan 8: introduction, definition of a quasicoherent sheaf (6.1-6.2)

Jan 13-15: locally free sheaves and coherent sheaves, Geometric Nakayama's Lemma (6.4, 14.1-14.3)

Jan 20-22: effective Cartier divisors and Weil divisors (15.1, 15.4, 15.6)

Jan 27-29: principal and locally principal Weil divisors, computing Picard groups, pulling back divisors, quasicoherent sheaves on projective schemes (15.4-15.5, 14.5.9, 14.6)

Feb 3-5: line bundles as maps to projective space, the Curve-to-Projective Extension Theorem (15.2-15.3)

Feb 10-12: globally generated sheaves, (very) ample line bundles (16.1-16.2)

Feb 17-19: relative Spec and Proj, intro to Cech cohomology (17.1-17.3, 18.1-18.3)

Feb 24-26: more Cech cohomology, Euler characteristic, genus, Riemann-Roch (18.1-18.4)

March 10-12: Hilbert polynomials, intro to classifying curves (18.5-18.6, 19.1-19.3)

March 17-19: Curves, week 2 (19.4-19.8)

March 24-26: Curves, week 3 + intro to differentials + in-class exam (Mar 26) (19.9-19.10, 21.1)

March 31-April 2: Differentials (21.1-21.3)

April 7-9: a little Hodge theory, ramification, Riemann-Hurwitz (21.4-21.7)

April 14-21: 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