MAT4215 – Algebraic Geometry II
Schedule, syllabus and examination date
Algebraic geometry is a classical subject, which in its modern form is described by scheme theory. The course provides an introduction to the theory of sheaves and schemes, and how the geometry of these can be studied using commutative algebra and sheaf cohomology.
After completing the course you will:
- understand the definitions and basic properties of affine and projective schemes;
- know the correspondence between homomorphisms between rings and affine schemes;
- know the construction of fiber products;
- know the basic properties of coherent sheaves and be able to do computations with them;
- be able to use Cech cohomology to calculate sheaf cohomology;
- know the connection between divisors, line bundles, and rational maps.
Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.
If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.
Recommended previous knowledge
- 10 credits overlap with MAT9215 – Algebraic Geometry II
- 10 credits overlap with MAT4220 – Algebraic geometry II (discontinued)
*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department.
6 hours of lectures/exercises every week extending over the
second half of the spring term.
Final oral examination.
Examination support material
No examination support material is allowed.
Language of examination
Subjects taught in English will only offer the exam paper in English.
You may write your examination paper in Norwegian, Swedish, Danish or English.
Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.
Explanations and appeals
Resit an examination
Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.
Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.
Withdrawal from an examination
It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.
Special examination arrangements
Application form, deadline and requirements for special examination arrangements.
The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.