MATH552 ALGEBRAIC GEOMETRY II
| Course Code: | 2360552 |
| 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
The aim of this course is to establish further properties of schemes and their morphisms, and if time permits to develop the cohomology of coherent sheaves on them. Applications of these techniques to classical geometrical problems will be discussed.
Course Content
Review of sheaves; quasi-coherent and coherent sheaves, direct and inverse images. Proper morphisms, quasi-coherent sheaves on projective schemes, projective morphisms. Cohomology of sheaves, cohomology of a projective scheme, higher direct images. Geometric applications.
Course Learning Outcomes
By the end of this course the student is expected to have mastered the various properties of schemes and morphisms between them, as well as cohomology of sheaves (if time permits).
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