Math 431 Algebraic Geometry
Fall 2002

Instructor: Ali Sinan Sertöz, Department of Mathematics
Room: SA-121, Phone: 1490
Office Hours: Tuesday 13:40-15:30

Text: Philip A. Griffiths, Introduction to Algebraic Curves, American Mathematical Society, 1989.

MONDAY 13:40-15:30 SAZ-19
WEDNESDAY 14:40-15:30 SAZ-19



1 23 Sep-25 Sep Algebraic Curves in the plane:   I.1, I.2, I.3
2 30 Sep-2 Oct Functions and forms: I.4, I.5, I.6
3 7 Oct-9 Oct Complex manifolds: I.7, I.8, I.9, I.10
4 14 Oct-16 Oct Singular curves: II.1, II.2, II.3
5 21 Oct-23 Oct Normalization theorem: II.4, II.5, II.6
6 28 Oct-30 Oct Bezout's theorem: II.7, II.8, II.9
7 4 Nov-6 Nov Differentials: III.1, III.2, III.3
8 11 Nov-13 Nov Riemann-Roch theorem: III.4, III.5
9 18 Nov-20 Nov Curves of genus 0 and 1: IV.1, IV.2
10 25 Nov-27 Nov Canonical maps: IV.3, IV.4
11 2 Dec (Wed!) Hyperelliptic curves: IV.5, IV.6, IV.7
12 9 Dec-11 Dec Abel's theorem: V.1
13 16 Dec-18 Dec Riemann bilinear relation: V.2, V.3
14 23 Dec-25 Dec Jacobi inversion theorem: V.4
15 30 Dec Applications: V.5

How to study:
Read the text lightly first. Then study the Examples. Construct your own examples and write them out explicitly. Test all new theorems against your examples to check if  they make sense. Check all conjectures, guesses and new ideas against your examples.  Then study some of the important proofs. Discuss with your friends to find out what they make of geometry!

Homework I   (10%): Due on 11 October 2002 Friday.            Solution
Homework II  (10%): Due on 1 November 2002 Friday.           Solution    
Homework III (10%): Due on 3 January 2003 Friday.               Solution
Midterm I        (20%): On 2 November 2002 Saturday.            Solution
Midterm II       (20%): On 14 December 2002 Saturday.           Solution
Final                 (30%): On 8 January 2002 Wednesday            Solution
                                    15:30 : SAZ-19