Modern Algebraic Geometry 2

 The course is a continuation of the course: Modern Algebraic Geometry 1, that was given in the first semester. It is a course on algebraic varieties over an algebraically closed field, using the technique of sheaves. Algebraic schemes will be mentioned briefly. We shall cover most of the standard material, with some additional glances into more advanced or specialized topics. The content of the course will be adapted to the background and capabilities of the registered students. The topics listed below are for both semesters.

Topics:

1. Categories and functors (interspersed among other topics).
2. Topological spaces equipped with sheaves of rings of functions, including non-algebraic examples.
3. Recalling commutative algebra.
4. Affine algebraic varieties.
5. Projective algebraic varieties.
6. Separability and algebraic varieties.
7. Survey of algebraic schemes.
8. Sheaves of modules.
9. Vector bundles.
10. Line bundles and the Picard group.
11. Types of maps between varieties.
12. Enumerative geometry and the Bezout Theorem.
13. Sheaf cohomology.
14. Algebraic groups.