Schedule, syllabus and examination date

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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

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.

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 half the spring term. The subject is taught as a part of MAT4215 – Algebraic Geometry II.

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.