Schedule, syllabus and examination date

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Changes in the course due to coronavirus

Autumn 2020 the exams of most courses at the MN Faculty will be conducted as digital home exams or oral exams, using the normal grading scale. The semester page for your course will be updated with any changes in the form of examination.

See general guidelines for examination at the MN Faculty autumn 2020.

Course content

Introduction to algebraic curves and varieties.

Algebraic geometry is a classical subject with a modern face that studies geometric objects defined by polynomial equations in several variables.

The course introduces the basic objects in algebraic geometry: Affine and projective varieties and maps between them. It covers the concepts of dimension, singularities, curves and intersection theory form a geometric and an algebraic point of view. There is a particular emphasis on concrete examples.

Learning outcome

After completing the course you:

  • know the definitions and basic properties of algebraic varieties;
  • know the relation between dimension in commutative rings and in algebraic sets;
  • can perform computations with morphisms and rational maps between algebraic varieties;
  • can decide whether an algebraic variety is singular;
  • can use blowing up to resolve plane curve singularities;
  • know the properties of the Hilbert polynomial and can compute it for selected projective varieties;
  • know the Bezout theorem and can use it in geometric applications;
  • know how to present, on a scientific level, a short thesis on a chosen topic of relevance, selected in collaboration with the lecturer.

Admission to the course

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.

MAT3200 – Commutative algebra (discontinued)/MAT4200 – Commutative Algebra.

Overlapping courses


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

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

Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.


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.

Resit an examination

This course offers both postponed and resit of examination. Read more:

Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Oct. 25, 2020 1:17:29 PM

Facts about this course

Teaching language