MAT4210 – Algebraic Geometry I
Schedule, syllabus and examination date
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.
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.
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.
Recommended previous knowledge
- 10 credits overlap with MAT4220 – Algebraic geometry II (discontinued).
- 10 credits overlap with MAT9210 – Algebraic Geometry I.
- 5 credits overlap with MAT4240 – Elliptic curves.
- 5 credits overlap with MAT9240 – Elliptic Curves.
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.
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.
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: