Exams after the reopening

As a general rule, exams will be conducted without physical attendance in the autumn of 2021, even after the reopening. See the semester page for information about the form of examination in your course. See also more information about examination at the MN Faculty in 2021.

Course content

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. Introduction to algebraic curves and varieties.

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;
  • are familiar with applications of algebraic methods in geometry.

Admission to the course

Students admitted at UiO must apply for courses in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.

Nordic citizens and applicants residing in the Nordic countries may apply to take this course as a single course student.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.

MAT4200 – Commutative Algebra

Overlapping courses

Teaching

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

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

Examination

Final oral exam which counts 100 % towards the final grade.

This course has 1 mandatory assignment that must be approved before you can sit 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 scale from A to F, where A is the best grade and F is a fail. 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. 21, 2021 7:43:46 PM

Facts about this course

Credits
10
Level
Master
Teaching
Spring
Examination
Spring
Teaching language
English