Algebraic Geometry I and II, 2004-2005

Instructor: Y.-P. Lee, JWB 305
Office Hours: MW 11-11:50 + any time my office door is open.

Class Time.
Fall: MWF 12:50-13:50 and Tue 14:00-15:00.
Spring: MWF 12:50-13:50 and Tue 14:30-15:30. (Usually lectures on MW and problem sessions on TF.)
Classroom.
Fall: JWB 308.
Spring: LCB 225 (MWF) and LCB 222 (Tue)

Course Website: http://www.math.utah.edu/~yplee/teaching/ag/
Text: Algebraic Geometry by Robin Hartshorne.
Also recommended: The Red Book of Varieties and Schemes by David Mumford.
Official Course Numbers. Fall: 6130-1 (24488), Spring: 6140-1 (13000).

Course Description: This will be a 2-semester series of Introduction to Algebraic Geometry. The first two chapters of the textbook will be the focus of the first semester. Chapter 3 (and hopefully more) will be covered in the second semester.

There will be 2 hours of lectures and 2 hours of problem sessions per week. Because I believe strongly in active learning, the problem sessions will be the core of the class. The pace of the lectures will be generally brisk and the students are expected to work hard outside the classroom. The participants of the lectures should plan to study at least 1 hour per lecture to keep up with the class. Those who plan to participate in the problem sessions should expect to invest a lot more (and perhaps learn a lot more in return)!

Regarding Commutative Algebra: My policy on the purely algebraic results is consistent with the textbook. Namely, these results will be quoted as needed, with references to the literature for their proofs. My suggestion to the students, if they have not seen these results before, is to skip back and forth between the textbook (or course notes) and books on commutative algebra, using the geometric examples to enrich the algebra, and the clean-cut algebraic techniques to clarify the geometry. Nevertheless, it is very useful to have basic working knowledge of commutative algebra, at the level of Introduction to Commutative Algebra by Atiyah and Macdonald, before plunging into Hartshorne's book.

Prof. Paul Roberts is teaching a class on commutative algebra, using the textbook by Matsumura. Students are encouraged to take his class concurrently.

Homework: Problem solving is vital for this class. We will try to work on as many problems as possible from the textbook. I will actively seek groups of volunteers to report their solutions in the problem sessions. (Hints to some problems are available upon request.)
Exams: No exam.
Grading Policy: In accordance with the departmental tradition, A is given to all registered students.

• (24 Mar 2005) 1. I have updated the rotation table. Please check out your problems. Just try them. It is perfectly OK if you can't do all. 2. There will be no class next week (28 Mar - 1 Apr). Enjoy the one week break!
• (12 Feb 2005) The Tuesday class on 15 Feb is cancelled due to a job talk.
• (18 Jan 2005) 1. The classroom and time on Tuesdays have been changed (yet again!) to LCB 222 / 14:30-15:30. 2. Presentation table is updated. 3. Problem session tomorrow.
• (16 Dec 2004) The classrom on Tuesday has been changed to LCB 323 due to the undergraduate colloquium.
• (29 Nov 2004) The classrooms for the Spring semester is LCB 225 (MWF) and LCB 215 (Tue).
• (3 Nov 2004) The Assignment table has been updated.
• (20 Oct 2004) A table of Ch. II excercise assignment is added.
• (18 Oct 2004) The MWF class time has changed to 12:50--13:50.
• (11 Oct 2004) No classes 25-27 Oct and 12-19 Nov.
• (29 Sep 2004) No classes on 4-5 October.
• (2 Sep 2004) Problem session will be held on Tuesday, 7 September.
• (25 Aug 2004) We decided to have problem sessions on Mondays and Wednesdays, starting next Monday, 30 August.
• (24 Aug 2004) The class schedule is finalized. (See above.)
• (15 Mar 2004) I also heartily recommend that those who have basic knowledge on algebraic geometry may start working on the problems in the textbook during the summer. Please feel free to drop by or email me if you have any questions. I have partial solutions/hints on some problems from Chapters 1 and 2.
• (6 Mar 2004) For those who are not familiar with commutative algebra, I strongly recommend that he or she goes through the book Introduction to Commutative Algebra by Atiyah and Macdonald before the class starts.