Schedule, syllabus and examination date

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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.

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.

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.

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 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.

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: MAT9215 – Algebraic Geometry II

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.

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. 21, 2021 7:43:48 PM

Facts about this course

Credits
10
Level
Master
Teaching
Spring

Taught according to demand and resources. Contact studieinfo@math.uio.no if you are interested in this course.

Examination
Spring
Teaching language
English