Schedule, syllabus and examination date

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Changes in the course due to coronavirus

Autumn 2020 the exams of most courses at the MN Faculty will be conducted as digital home exams or oral exams, using the normal grading scale. The semester page for your course will be updated with any changes in the form of examination.

See general guidelines for examination at the MN Faculty autumn 2020.

Course content

Algebraic geometry is a classical subject, which in its modern form is described by scheme theory. The course provides an introduction to the theory of sheaves and schemes, and how the geometry of these can be studied using commutative algebra and sheaf cohomology.

Learning outcome

After completing the course you will:

  • understand the definitions and basic properties of affine and projective schemes;
  • know the correspondence between homomorphisms between rings and affine schemes;
  • know the construction of fiber products;
  • know the basic properties of coherent sheaves and be able to do computations with them;
  • be able to use Cech cohomology to calculate sheaf cohomology;
  • know the connection between divisors, line bundles, and rational maps;
  • 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 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.

MAT3200 – Commutative algebra (discontinued)/MAT4200 – Commutative Algebra and MAT4210 – Algebraic Geometry I

Overlapping courses

Teaching

6 hours of lectures/exercises every week extending over the second half of 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 examination.

In addition, each PhD candidate 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.

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 pass/fail scale. 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. 25, 2020 1:17:29 PM

Facts about this course

Credits
10
Level
PhD
Teaching
Spring
Examination
Spring
Teaching language
English