Algebraic Geometry (AlgGeo)

Course content

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.


MSc Programme in Mathematics

MSc Programme in Mathematics with a minor subject

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.

5 hours lectures and 4 hours exercises each week for 7 weeks

Advanced vector spaces (AdVec), knowledge about general topology and commutative algebra.

Academic qualifications equivalent to a BSc degree is recommended.

Feedback by final exam (In addition to the grade)

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 (30-minute preparation time)
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.

All aids allowed

All aids allowed during preparation

Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners

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 assessment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 142
  • Exercises
  • 28
  • Exam
  • 1
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

Block 4
No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Søren Galatius   (8-716b766b7e737f7d4a776b7e7238757f386e75)
Saved on the 14-02-2024

Are you BA- or KA-student?

Are you bachelor- or kandidat-student, then find the course in the course catalog for students:

Courseinformation of students