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
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.
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.
- ECTS
- 7,5 ECTS
- Type of assessment
-
Oral examination, 30 minutes
- Type of assessment details
- The student will have 30 minutes preparation before the exam.
- Aid
- 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 should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
Single subject courses (day)
- Category
- Hours
- Lectures
- 35
- Preparation
- 149
- Exercises
- 21
- Exam
- 1
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAK22018U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
- Duration
-
1 block
- Placement
- Block 4
- Schedulegroup
-
C
- Capacity
- no limit
The number of seats may be reduced in the late registration period - Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinator
- Søren Galatius (8-6e6873687b707c7a4774687b6f35727c356b72)
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