MAT9215 – Algebraic Geometry II
Schedule, syllabus and examination date
Changes in the course due to coronavirus Spring 2020
Teaching and examinations will take place digitally. This may result in changes to your schedule, mandatory activities, exam form and grading scale. See updated information on the semester page and in Canvas.
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.
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.
Recommended previous knowledge
- 10 credits overlap with MAT4215 – Algebraic Geometry II.
- 10 credits overlap with MAT4220 – Algebraic geometry II (discontinued).
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.
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.
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: