MODERN ALGEBRAIC GEOMETRY, FALL 2021, LECTURE AND HOMEWORK PLANS
[H]=Hartshorne; [V]=Vakil; [EH]=Eisenbud-Harris
- Week 1, August 24 and 26. This week's classes will be held by Zoom.
Reading for August 24. [H] Chapter I as needed. [H] Chapter II.1
Reading for August 26. [V] Chapters 1.1-1.6, 2
Homework problems (try to do by Wednesday, September 1): [H] II.1.1-II.1.22 (as many as you can!)
- Week 2, August 31 and September 2. This week's classes will be held by Zoom.
Reading for August 31. [H] Chapter II.2, [V] Chapters 3-4.
September 2: In-class problem session on [H] Chapter II.1 problems
Homework problems (try to do by Wednesday, September 8): finish the problems you couldn't do from [H] II.1.1-II.1.22. Start on problems from [H] II.2 if you finish those.
- Week 3, September 7 and 9. This week's classes will be held by Zoom.
No new reading for this week's classes. [H] Chapter II.2 and [V] Chapter 4
Read ahead for September 14: [EH] Chapter II.
Homework problems (try to do by Wednesday, September 15): finish the problems you couldn't do from [H] II.2.
- Week 4, September 14 and 16.
Class on September 14 will be held by Zoom. Class on September 16 will be held in-person in 143 Altgeld Hall
Reading for September 14: [H] II.3, II.4; [V] Chapters 5, 10, 11
Homework problems (try to do by Wednesday, September 22): [V] 4.4.A-F; 4.5.A,B. [EH] II-3, II-7. II-11, II-12.
- Week 5, September 21 and 23.
Class on Tuesday, September 21 will be held by Zoom. Class on Thursday, September 23 will be held in-person in 143 Altgeld Hall.
This week's lectures will focus on [H] II.3, II.4
Read ahead for week 6: [H] II.5; [V] as much of Chapters 13, 16 as you can.
Homework problems (try to do by Wednesday, September 29): [H] II.3.1-II.3.13, II.3.16-17. Read [H] II.3.20.
- Week 6, September 28 and 30. This week's classes will be held in-person in 143 Altgeld Hall.
This week's lectures will focus on [H] II.4, II.5.
Read ahead for week 7: [V] Chapters 14, 15, and (if you can!) 17.
Homework problems (try to do by Wednesday, October 6): [H] II.5.1-II.5.6, II.5.8, II.5.15, II.5.16, II.5.17.
- Week 7, October 5 and 7.
This week's lectures will focus on [H] II.5 and [V] Chapter 14.
Read ahead for week 8: [H] III.4, [V] Chapter 18
Homework problems (try to do by Wednesday, October 13): [H] II.5.7, II.5.18, II.7.1, II.7.2, II.7.5 (you will need to read the definitions of "ample" and "very ample" first).
- Week 8, October 12 and 14.
After finishing [H] II.5, this week's lectures will focus on [V] Chapter 14 and [H] III.4.
Read ahead for week 9: [H] III.5, [V] Chapter 18.3
Homework problems (try to do by Wednesday, October 20): [H] III.4.1-III.4.7, III.4.9, III.4.10
- Week 9, October 19 and 21.
This week's lectures will focus on [H] III.4 and III.5.
Read ahead for week 10: [H] II.6, [V] 8.4, 14.2, 14.3
Homework problems (try to do by Wednesday, October 27): [H] III.5.1-II.5.8
- Week 10, October 26 and 28.
This week's lectures will focus on the previously omitted parts of [H] II.6
Read ahead for week 11: [H] II.7
Homework problems (try to do by Wednesday, November 3): [H] II.6.1-II.6.5, II.6.12
- Week 11, November 2 and 4.
After finishing the last details about the group law on a cubic plane curve, this week's lectures will focus on previously omitted parts of [H] II.4 and start [H] II.7.
Read ahead for week 12: [V] Chapters 10, 15, 16.
Homework problems (try to do by Wednesday, November 10): [H] II.4.1-II.4.9.
- Week 12, November 9 and 11.
We will continue with projective morphisms, [H] II.7.
Read ahead for week 13: [H] IV.1-2; [V] Chapters 19.1-19.5
Homework problems (try to do by Wednesday, November 17): [H] II.7.3-4, II.7.8, II.7.10-11.
- Week 13, November 16 and 18.
After completing some material on projective morphisms ([H] II.7), most of the week will be spent starting on curves, following [H] IV and [V] Chapter 19. The material on curves will not be entirely self-contained, but will assume some results on cohomology and differentials which will be clearly stated but not proven until next semester. Here are references to [H] Chapter II.8 and Chapter III for the assumed material.
Read ahead for week 14: [H] Chapter IV; [V] Chapters 19
Homework problems (try to do by Wednesday, December 1): [H] IV.1.1-8
- Week 14, November 30 and December 2.
I would like to cover [H] IV.2, IV.3, and IV.5 by the end of the semester.
Homework problems: [H] IV.2.2-3, IV.3.1, IV.3.4, IV.3.6, IV.5.1, IV.5.6. I don't expect that there will be time to go over any of these in class.
- Week 15, December 7.
[H] IV.5. See Harris and Morrison, Moduli of Curves to follow up on topics related to moduli of curves (which will not be covered next semester)