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
  • 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 Faculty of Mathematics and Natural Sciences at 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.

Overlapping courses

Teaching

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.

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.

In addition, each PhD candidate is expected to give an oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer before you can sit the final exam.

It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: MAT4210 – Algebraic Geometry I

Examination support material

No examination support material is allowed.

Language of examination

Courses 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:

More about examinations at UiO

You will find further guides and resources at the web page on examinations at UiO.

Last updated from FS (Common Student System) Nov. 9, 2024 8:15:14 PM

Facts about this course

Level
PhD
Credits
10
Teaching
Spring
Examination
Spring
Teaching language
English