Math 818, Algebra and Geometry, Fall 2010
Math 818 is a graduate beginning algebraic geometry course. Lectures are 10:30  12:20, Tuesdays and Thursdays in AQ 5020.
Announcements
 If you would like to know more about abelian varieties in a language which is more sophisticated than what we've been using, but not hopelessly so, please look at Milne's course notes.
 The written project is due Dec 7 (in my mailbox).
 The schedule for the presentations is:
 Nov 30
 Jemma; Julian
 Dec 2
 Tom; Sam; James
 Office hours are Mondays 10:3011:30 and 2:303:30. You should also feel free to drop by whenever convenient.
 We will meet Thursday September 9 to decide amongst us what topics to cover and how you will be evaluated. Regular lectures will begin Tuesday September 14.
Assignments
By popular demand the homework questions will dribble in. When we get to 10 or so we'll set a due date and repeat.

Due Thursday Oct 7 in class. Solutions.
 Shafarevich I.2.5, I.2.11, I.2.15.
 Fulton 110, 126.
 Shafarevich I.3.4, I.3.6.
 Draw a diagram illustrating the relationships between the algebraic set picture, the ideal picture, coordinate ring picture, and the function field picture in the affine case. Try to include as many relationships as we've discussed and to make it a clear and useful big picture view of what we've learned so far.
 Fulton 418, 420 (see chapter 2 section 6 for the star notation, which is not the same as in question 418).

Due Thursday Oct 28 in class. Solutions.
 Shafarevich I.4.9
 Shafarevich I.5.7, I.5.8
 Fulton 32, 38, 313
 Fulton 320
 Fulton 53, 56, 522
 Due Thursday November 18. Solutions.
 Shafarevich I.6.6, I.6.7, I.6.8, II.1.1
 Fulton 72. F' means blow up the singularity.
 Shafarevich II.4.4
 Shafarevich III.1.2, III.1.5
 Shafarevich III.1.12, III.1.18

Due Thursday December 2. Solutions.
 Consider Fulton's and Shafarevich' proofs of Bezout's theorem for curves (Fulton 5.3, Shafarevich III.2.2). Are they fundamentally the same proof in different languages or do they have really different ideas? If they are different summarize the key ideas of each in a few lines. If they are the same provide a dictionary to translate the language and notation between them.
 Fulton 810, 814 parts a and b.
 Shafarevich III.3.1
And that's all.
Information
Outline (in pdf format).
 Instructor:
 Karen Yeats
 Office:
 SC K 10508
 Email:
 karen_yeats at sfu.ca
 Office Hours:
 Mondays 10:3011:30 and 2:303:30.
 Lectures:
 10:3012:20 Tuesdays and Thursdays AQ 5020
 Textbooks:
 Shafarevich Basic Algebraic Geometry 1 and Fulton Algebraic Curves.