CANCELLED Rational Surfaces

Course content

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.


MSc Programme in Mathematics

Learning outcome

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.

5 hours lectures and 3 hours exercises each week for 7 weeks

Knowledge about Algebraic Geometry

7,5 ECTS
Type of assessment
Oral examination under invigilation
Oral examination, 30 min
The student will have 30 minutes preparation before the exam.
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners.
Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 35
  • Exercises
  • 21
  • Exam
  • 1
  • Preparation
  • 149
  • English
  • 206