The syllabus for Math 631 (Algebraic Geometry I) is available here.

The current office hours schedule is: Mon 2pm-3pm in EH 3842, Wed 8pm-9pm on Zoom (link in syllabus above), Thu 3pm-4pm in EH 3842.

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 (and possibly Gradescope).

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 and submit them on Gradescope (linked on Canvas) for a grader to look at. I am also happy to answer questions about specific problems by e-mail (address in the linked syllabus above) or in office hours.

Problem Set 0 (posted Thursday, August 28)

Problem Set 1 (posted Thursday, September 4)

Problem Set 2 (posted Thursday, September 11)

Problem Set 3 (posted Thursday, September 18)

Problem Set 4 (posted Thursday, September 25)

Problem Set 5 (posted Thursday, October 2)

Problem Set 6 will be posted on Thursday, October 9.

Rough schedule (with section numbers from FoAG):

Aug 26-28: introduction to course, presheaves, sheaves, pushforwards, stalks (2.1-2.2)

Sep 2-4: categories of (pre)sheaves, sheafification, abelian categories (2.3-2.4, 2.6).

Sep 9-11: Spec A (as a set and topological space), functoriality (3.1-3.5)

Sep 16-18: topological properties of Spec A, the dictionary between ring theory and scheme theory, the structure sheaf (3.6-3.7, 4.1)

Sep 23-25: schemes, locally ringed spaces, non-affine schemes, the projective line, morphisms of schemes (4.3-4.4, 7.1-7.2, some of 7.3)

Sep 30-Oct 2: A-schemes, A-valued points, reduced and non-reduced schemes, integral schemes (the rest of 7.3, some of 5.2)

Oct 7-9: more with integral schemes, projective space, Proj (5.2, 4.4.9, 4.5)

Oct 16: maps of projective schemes, the definition of closed embeddings (7.4, a little of 9.1)

Oct 21-23: Fiber products of schemes, fibers of morphisms (10.1-10.3)

Oct 28-30: closed embeddings, Bezout's theorem, the Veronese embedding, the Segre embedding (9.1, 9.3, 10.6)

Nov 4-6: assorted properties of schemes and morphisms (5.1, 5.3, 8.1-8.3)

Nov 11-13: separated morphisms, the category of k-varieties and rational maps, proper morphisms (11.1-11.4, 7.5.6)

Nov 18-20: in-class exam (Nov 18), dimension and codimension (12.1-12.4)

Nov 25: tangent spaces, regularity, curve singularities (13.1-13.3, 5.4)

Dec 2-4: the Jacobian criterion, Bertini's theorem, DVRs, Algebraic Hartogs's Lemma, definition of the class group (13.3-13.5, 15.4.10)