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;
  • present, on a scientific level, a short thesis on a chosen topic of relevance, selected in collaboration with the lecturer.


PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.

Overlapping courses

10 credits overlap with MAT4215 – Algebraic Geometry II

*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.

In addition, each PhD candidate is expected to give a one hour oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer for the student to be admitted to the final exam.

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 pass/fail scale. 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.

Facts about this course






Every spring


Every spring

Teaching language


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