Algebraic Geometry (AlgGeo)
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.
MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject
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.
5 hours lectures and 3 hours exercises each week for 7 weeks
Knowledge about general topology and commutative algebra.
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 minutes
- Type of assessment details
- The student will have 30 minutes preparation before the exam.
- 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
- No external censorship
Criteria for exam assessment
The student must in a satisfactory way demonstrate that they have mastered the learning outcome of the course.
Single subject courses (day)
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- Block 4
- no limit
The number of seats may be reduced in the late registration period
- Study Board of Mathematics and Computer Science
- Department of Mathematical Sciences
- Faculty of Science
- Søren Galatius (8-6a646f64776c7876437064776b316e7831676e)
- Mikala Ørsnes Jansen (6-607c7e747f74538074877b417e8841777e)
Mikala Ørsnes Jansen
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