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: | |
| 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).