Schedule, syllabus and examination date

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Course content

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.

Learning outcome

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.

Admission

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.

Prerequisites

Recommended previous knowledge

MAT4200 – Commutative Algebra and MAT4210 – Algebraic Geometry I.

Overlapping courses

*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department. 

Teaching

6 hours of lectures/exercises every week extending over the
second half of the spring term.

Examination

1 mandatory assignment.

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.

Grading scale

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.

Evaluation

The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course

Credits

10

Level

Master

Teaching

Every spring

Examination

Every spring

Teaching language

English

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.