2006 Fall
Ali Sinan
Sertöz
Faculty of Science, Department of Mathematics, Room: SA-121
Office Hours: Wednesday 13:40-15:30 or by appointment
Schedule:
MON 15:40-17:30 SAZ-02
WED 9:40-10:30 SAZ-21
Synopsis:
This is an introductory lecture to algebraic geometry. We will assume
nothing beyond a reasonable undergraduate education. Formally I intend to
proceed along the lines of the book "An Invitation to Algebraic Geometry"
but depending on the enthusiasm and the motivation of the class I may cover some
cohomology, Riemann-Roch theorems and some classification theorems of curves and
even of surfaces. Mentioning of the classification of threefolds need not be
excluded either! For every extra subject I will provide class notes.
Recommended Text Books:
Karen E. Smith et al, An Invitation to Algebraic Geometry, Springer, 2000.
J. Harris, Algebraic Geometry, Springer, 1992.
R. Hartshorne, Algebraic Geometry, Springer, 1977.
Intended Subjects to be Covered
(This may change with class feedback.)
| WEEK-1 | Affine varieties |
|---|---|
| WEEK-2 | Commutative algebra |
| WEEK-3 | Projective varieties |
| WEEK-4 | Quasi-projective varieties |
| WEEK-5 | Classical constructions |
| WEEK-6 | More classical constructions |
| WEEK-7 | Smoothness |
| WEEK-8 | Singularities |
| WEEK-9 | Resolution of singularities |
| WEEK-10 | Introduction to curves |
| WEEK-11 | Classification of curves |
| WEEK-12 | Introduction to surfaces |
| WEEK-13 | Line bundles and vector bundles |
| WEEK-14 | Sheaves |
| WEEK-15 | Sheaf cohomology and examples |
Grading and Exams:
| Homeworks | 30% | ||||
| Take-Home Midterm | 30% | ||||
| Take-Home Final | 40% |
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.
Notes and Homework:
Affine Varieties