Geometry of Schemes



We intend to cover the first half of “The Geometry of Schemes” by Eisenbud and Harris, linked below. I’ve slowed down the pace in order to make room for Vakil’s online AG course, which I think would be nice to do concurrently. If you’d like to be kept updated, please join the mailing list which I think you may be able to do at the bottom of this page.


Date Leader Reading Problems
Week 1 (May 29, Jun 2) John Cobb I.1 Affine Schemes 5, 7, 9, 10, 20, 21
Week 2 (Jun 5, Jun 9) Tejasi Bhatnagar I.2 Schemes in General 24, 25, 30, 31, 34, 32, 37, 44, 45
Week 3 (Jun 12, Jun 16) John Cobb I.3 Relative Schemes 46, 47, 48, 50, 51
Week 4 (Jun 19, Jun 23) Daniel Levitin II.1-II.2 Reduced Schemes 2, 3, 6, 7, (maybe 8)
Week 5 (Jun 26, Jun 30) Ivan Aidun II.3.1-II.3.4 Nonreduced Schemes 11, 15, 14, 22
Week 6 (Jul 3, Jul 7) John Cobb II.3.4-II.3.5 Nonreduced Schemes 25, 31, 33, 35
Week 7 (Jul 10) Daniel Erman Q&A Break Come up with questions!
Week 8 (Jul 14, Jul 17) Ivan Aidun II.4 Arithmetic Schemes 36, 38, 40, 44
Week 9 (Jul 21, Jul 24, Jul 28) Tejasi Bhatnagar III.1-III.2.3 Attributes of Morphisms 1, 2, 3, 4, 6, 12, 15

From here, the group has decided that it will be more worthwhile at this point to pick up with another book after taking our qualifying exams, likely Vakil’s notes.

Pushed off schedule: III.2.4-III.2.8 Proj of a Graded Ring, III.3.1-III.3.4 Invariants of Projective Schemes, III.3.5-III.3.6 Invariants of Projective Schemes & IV.1 Flexes of Plane Curves

If we have the time, covering V.1-V-2 Images and Resultants or VI.1 The Functor of Points would be good.

General Meeting Structure

We will meet Tuesdays at 1:00pm and Fridays at 1:00pm (CST) via Zoom for about an hour, with the following goals in mind:

Obviously two meetings every week can be a lot, so no one should feel like they have to attend every single meeting. However, I think it will work best if everyone comes as much as possible.

Google Forum

While going through the settings of our new google group, I found a way to embed a whole forum system. I’ve included it below in case it turns out to be helpful.