NMAK16016U CANCELLED Rational Surfaces
MSc Programme in Mathematics
Roughly speaking, rational surfaces are surfaces which can be parametrized by two parameters. Their geometry is very explicit, but it is also very rich, so these surfaces provide very nice examples which we can apply many techniques from algebraic geometry. Also one can consider many arithmetic problems regarding rational surfaces.
This course will be an introduction to theory of rational surfaces. It will cover the following topics:
Cohomology of line bundles, intersection theory on surfaces, blow ups and the contractibility criterion, del Pezzo surfaces, Castelnuovo’s theorem, the minimal model program in dimension 2, classification of minimal rational surfaces over a non-closed field, rational points over function fields.
Knowledge: To display knowledge and understanding of the course
topics
and content at a level suitable for further studies in algebraic
and arithmetic geometry
Skills: At the end of the course the student is expected to be able
to
follow and reproduce arguments at a high abstract level
corresponding to
the contents of the course.
Competences: At the end of the course the student is expected to
be
able to apply basic techniques and results to concrete
examples.
- Category
- Hours
- Exam
- 1
- Exercises
- 21
- Lectures
- 35
- Preparation
- 149
- Total
- 206
As
an exchange, guest and credit student - click here!
Continuing Education - click here!
- Credit
- 7,5 ECTS
- Type of assessment
- Oral examination under invigilationOral examination, 30 min
The student will have 30 minutes preparation before the exam. - Exam registration requirements
To be eligible to take the exam the student must have handed in the mandatory homework assignment, and this must have been approved.
- Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners.
- Re-exam
The same as the ordinary exam.
To be eligible to take the re-exam, students who have not already had the mandatory assignment approved must re-submit the assignment no later than 2 weeks before the re-exam week. The mandatory assignment must be approved in order to take the re-exam.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Course information
- Language
- English
- Course code
- NMAK16016U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- C
- Course capacity
- No restrictions/ no limitations
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Sho Tanimoto (3-796e754673677a6e34717b346a71)