NMAK14005U  Algebraic Geometry (AlgGeo)

Volume 2017/2018

MSc Programme in Mathematics


Algebraic Geometry is the study of geometric structures arising from
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.

Learning Outcome

Knowledge: To display knowledge and understanding of the course topics
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.

Knowledge about general topology and commutative algebra.
5 hours lectures and 3 hours exercises each week for 7 weeks
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
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.

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 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.

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