MATH 431 - Algebraic Geometry
Spring 2010
What
is Algebraic Geometry & Math 431 ?
Ali Sinan Sertöz
Faculty of Science, Department of Mathematics, Room: SA-121
Office Hours: Wednesday 10:40-12:30,
SA-121
Text Books:
Elementary Algebraic Geometry, Klaus Hulek, American
Mathematical Society, 2003.
Recommended Text Books:
Algebraic Geometry, R. Hartshorne, (first chapter),
Springer-Verlag GTM Vol 52, 1977.
Schedule:
| This is a 3 credit course but we will nonetheless meet 2+2 hours each week. This will allow me to go more slowly than usual and solve more problems in class than I usually do. | |||
| TUE | 10:40-12:30 | SAZ19 | |
| FRI | 08:40-10:30 | SAZ19 | |
Attendance:
| Attendance is a must. I will read homework and exam papers of class-regulars with more tolerance than absentees. Shelves are full of algebraic geometry books but it is not enough to read them; you must hear how these concepts are interpreted. You must offer your own interpretations and check how others react. And you must ask questions immediately as it comes to your mind. Let one concept remain blurred and the rest is all lost. So you must be in class to be part of it. There is no alternative; attendance is a must. |
Exams and Grading:
| Midterm 1 | 25% | 5 March 2010 Friday 8:40 | Solutions | |
| Midterm 2 | 25% | 16 April 2010 Friday 8:40 | Solutions | |
| Final | 25% | 24 May 2010 Monday 12:15 | SAZ18 | Solutions |
| Homework | 25% | |||
| Make-up Exam | ||||
| Seeing Exam Papers | ||||
Syllabus:
| Week |
Date |
Subjects to be covered | Chapter |
| 1 | 29 Jan | Introduction | 0 |
| 2 | 2, 5 Feb | Affine Varieties | 1.1 |
| 3 | 9, 12 Feb | Affine regular and rational maps | 1.2, 1.3 |
| 4 | 16, 19 Feb | Projective varieties | 2.1, 2.2 |
| 5 | 23, 26 Feb | Projective regular and rational maps | 2.3 |
| 6 | 2 Mar | Review | |
| 6 | 5 Mar | Midterm Exam I | |
| 7 | 9, 12 Mar | Smooth versus singular | 3.1 |
| 8 | 16, 19 Mar | Dimension - Plane curves | 3.2, 4.1 |
| 9 | 23 Mar | Intersection multiplicity | 4.2, |
| 10 | 30 Mar, 2 Apr | Elliptic curves | 4.3, 4.4 |
| 5-9 Apr | Spring break | ||
| 11 | 13 Apr | Review | |
| 11 | 16 Apr | Midterm Exam II | |
| 12 | 20 Apr | Divisors on curves | 6.1 |
| 13 | 27, 30 Apr | Bezout's theorem | 6.2, 6.3 |
| 14 | 4, 7 May | Linear systems | 6.4 |
| 15 | 11, 14 May | Projective embeddings | 6.5 |
Old Exams:
Old exams are available on the Old Courses Web Page but since each time I teach this course I teach it in a different way, none of the old exams will make sense for this semester.
Contact address is: