Schedule, syllabus and examination date

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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 having completed the course

• you will understand the definitions and basic properties of affine and projective schemes

• you will know the correspondence between homomorphisms between rings and affine schemes

• you will know the construction of fiber products

• you will know the basic properties of coherent sheaves and be able to do computations with them

• you will be able to use Cech cohomology to calculate sheaf cohomology

• you will know the connection between divisors, line bundles, and rational maps

After having completed the course you will also be able 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.

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 the
second half of the spring term.

Examination

Final mark is given based 100% on 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.

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.

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.