Schedule, syllabus and examination date

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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

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.

Prerequisites

Formal prerequisite knowledge

None.

Recommended previous knowledge

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

Overlapping courses

*The information about the overlaps is not complete. Contact the Department for more information if necessary.

Teaching

6 hours of lectures/exercises every week extending over half the spring term. The subject is taught as a part of MAT4220.

Examination

Final oral examination.

In addition, each PhD student 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.

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.

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

PhD

Teaching

Every spring

Examination

Every spring

Teaching language

English

The course is given in English. If no students have asked for the course in English within the first lecture, it may be given in Norwegian.