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: | Assoc.Prof.Dr. EMRE COŞKUN |
| 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
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Gains academic maturity through self-study. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Carries out parts of a mathematical research program independently. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Gets exposed to academic culture through interaction with others. | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution