NMAK22018U Algebraic Geometry (AlgGeo)

Volume 2024/2025
Education

MSc Programme in Mathematics

MSc Programme in Mathematics with a minor subject

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.

Learning Outcome

Knowledge: To display knowledge and understanding of the course topics
and content at a level suitable for further studies in Algebraic
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.

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

Academic qualifications equivalent to a BSc degree is recommended.
5 hours lectures and 4 hours exercises each week for 7 weeks
  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 142
  • Exercises
  • 28
  • Exam
  • 1
  • Total
  • 206
Written
Oral
Individual
Collective
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.

Credit
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.

Aid
All aids allowed

All aids allowed during preparation

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

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