MATH 431 - Algebraic Geometry
Spring 2011
Ali Sinan Sertöz
Faculty of Science, Department of Mathematics, Room: SA-121
Office Hours: Wednesday 10:40-12:30,
SA-121
Text Books:
Philip A. Griffiths, Introduction to Algebraic Curves, American
Mathematical Society, 1989.
Recommended Text Books:
Robin Hartshorne, Algebraic Geometry, (first chapter),
Springer-Verlag GTM Vol 52, 1977.
Rick Miranda, Algebraic Curves and Riemann Surfaces, American
Mathematical Society, 1995.
Frances Kirwan, Complex Algebraic Curves, Cambridge University Press, 1992.
Schedule:
| This is a 3 credit course and we will meet 2+1 hours each week. On Friday, the second hour, I will organize an optional student seminar on algebraic geometry, after which we will join the ODTU-Bilkent Algebraic Geometry Seminar, either here or at ODTU. | |||
| TUE | 15:40-17:30 | SAZ-18 | |
| FRI | 13:40-14:30 | SAZ-18 | |
Attendance:
| Attendance is a must. I will take attendance in class and take it seriously. |
Exams and Grading:
| Midterm 1 | 25% | Solutions | ||
| Midterm 2 (*) | 25% | |||
| Final | 25% | Solutions | ||
| Homework | 25% | HWK1-solutions | HWK2-solutions | HWK3-solutions |
| (*) Midterm 2 consisted of exercises 5.1, 5.2, 5.3 and 5.4 on pages 122-124. There are extensive hints after these exercises so I do not give a detailed solution here. | ||||
Syllabus:
| Week |
Date |
Subjects to be covered | Chapter |
| 1 | Feb 1-Feb 4 | Riemann Surfaces | I |
| 2 | Feb 8-Feb 11 | Functions and forms | I |
| 3 | Feb 15-Feb 18 | Poincare-Hopf formula | I |
| 4 | Feb 22-Feb 25 | Algebraic Varieties | I |
| 5 | Mar 1-Mar 4 | Singularities | II |
| 6 | Mar 8 | Review | |
| 6 | Midterm Exam I | ||
| 6 | Mar 11 | Weierstrass Polynomial | II |
| 7 | Mar 15-Mar 18 | Divisors | II |
| 8 | Mar 22-Mar 25 | Bezout theorem | II |
| 9 | Mar 29-Apr 1 | Riemann-Hurwitz theorem | III |
| 10 | Apr 5-Apr 8 | Genus formula | III |
| Apr 11-Apr 15 | Spring break | ||
| 11 | Apr 19-Apr 22 | Riemann-Roch theorem | IV |
| 12 | Apr 26 | Genus 0 and 1 cases | |
| 12 | Midterm Exam II | ||
| 12 | Apr 29 | Higher genus cases | IV |
| 13 | May 3-May 6 | Abel's theorem | V |
| 14 | May 10-May 13 | Jacobi inversion theorem | V |
Old Exams:
I used this book also in 2002. You can refer to that year's web page of Math 431 for old exams and homeworks.
Contact address is: