NMAK14005U Algebraic Geometry (AlgGeo)
MSc Programme in Mathematics
Algebraic Geometry is the study of geometric structures arising
solution sets of polynomial equations, and forms a central part of
modern mathematics. It has numerous applications, ranging from number
theory to theoretical physics.
The course will be an introduction to Algebraic Geometry, and will
cover the following topics:
Algebraic sets, affine and projective varieties, fundamental properties
of varieties. Sheaves and locally ringed spaces. Morphisms of varieties, birational maps and blow-ups. Smoothness and singularities. Hilbert polynomials and Bezout's theorem.
Knowledge: To display knowledge and understanding of the course
and content at a level suitable for further studies in Algebraic
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.
Academic qualifications equivalent to a BSc degree is recommended.
Written feedback will be given on the mandatory assignment. Oral feedback will be given on students’ presentations in class. Individual feedback will be given via corrections to the mandatory assignment, as well as in connection with the oral exam. Collective feedback will be given through comments by the TA on blackboard presentation by students at the exercise sessions.
- 7,5 ECTS
- Type of assessment
- Oral examination, 30 minutesThe 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.
- Only certain aids allowed
All aids allowed for the preparation.
For the oral exam, the student may bring 1 A4 sheet of notes.
- Marking scale
- 7-point grading scale
- Censorship form
- External censorship
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. The mandatory assignment must be approved no later than three weeks before the re-exam week.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.