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 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.
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 (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 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
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 limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
- Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinators
- Jesper Grodal (2-79764f7c7083773d7a843d737a)
- Elisenda Feliu (6-6a6b6a716e7a457266796d33707a336970)
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Courseinformation of students