MATH776 COHERENT SHEAVES IN ALGEBRAIC GEOMETRY
| Course Code: | 2360776 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
Coherent sheaves and derived categories form an indispensable component of every researcher's toolbox in modern algebraic geometry. The objective of this course is to give students the basics of these tools.
Course Content
Semi-stability, stability, Harder-Narasimhan filtration. Families of sheaves, moduli spaces. Construction methods. The derived category of the abelian category of coherent sheaves. Quiver representations and the Bondal correspondance with the derived category of the abelian category of coherent sheaves.
Course Learning Outcomes
By the end of the course, a student will have learned:
- Chern classes of coherent sheaves and how to calculate them
- construction methods for coherent sheaves
- properties of moduli spaces of sheaves
- definition and properties of derived categories
- quivers and quiver representations, Gabriel's theorem, relations to derived categories of algebraic varieties