Math 431 Algebraic Geometry
2008 Spring Semester
Ali Sinan Sertöz
Faculty of Science, Department of Mathematics, Room: SA-121
Office Hours: Wednesday 13:40-15:30
Text Book:
1) Miles Reid, Undergraduate Algebraic Geometry,
Cambridge University Press., 1988, corrected printing 2001.
2) Class notes will be provided on this site for additional
material to be covered.
Schedule:
| MON | 13:40-15:30 | SAZ20 | |
| THU | 13:40-14:30 | SAZ20 |
Syllabus:
| Week |
Date |
Subjects to be covered | Chapter |
| 1 | 11-13 Feb | Plane conics | I |
| 2 | 18-20 Feb | Plane cubics and the group law | I |
| 3 | 25-27 Feb | Curves and their genus, an introduction | I |
| 4 | 3-5 Mar | Affine varieties | II & Notes |
| 5 | 10-12 Mar | Hilbert's zero theorem | II & Notes |
| 6 | 17-19 Mar | Elementary topics from affine geometry Midterm | II & Notes |
| 7 | 24-26 Mar | Projective varieties | III & Notes |
| 8 | 31 Mar-2 Apr | Resolution of singularities | III & Notes |
| 9 | 7-9 Apr | Curve singularities | Notes |
| 10 | 14-16 Apr | Arf rings and Arf closure Midterm | Notes |
| 11 | 21 Apr | Curves and Riemann inequality | Notes |
| 12 | 28-30 Apr | Riemann-Roch theorem | Notes |
| 13 | 5-7 May | Hurwitz theorem | Notes |
| 14 | 12-14 May | Hyperelliptic curves | Notes |
| 15 | 20 May | Existence of curves of any genus | Notes |
Grading and Exams:
Homework problems will be assigned regularly.
You are encouraged to discuss solutions with your friends but you must write
your homework yourself.
It is not acceptable to borrow your friend's written homework or for that matter
to lend your written version.
Writing should be private.
However until that stage you may and in fact you should discuss solutions with
your friends, and even with me.
| Midterm 1 | 20% | 27 March 2008, 13:40, SAZ20 | Solutions |
| Midterm 2 | 20% | 14 April 2008, 13:40, SAZ20 | Solutions |
| Final | 30% | 21 May 2008, 9:00 SAZ01 | Solutions |
| Homeworks | 30% |
All homeworks and solutions will be announced here in Acrobat format (pdf) for which you need to download Acrobat Reader if that is not already installed on your machine.
For old exams and homeworks see my all courses page.
Here are my class notes. Read them gently and report any errors, inaccuracies, ambiguities or suggestions to me.