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.
4 hours lectures and 4 hours exercises per week for 9 weeks
Knowledge of advanced linear algebra (e.g., obtained through the
UCPH MSc course Advanced vector spaces (AdVec)).
Knowledge about general topology (e.g., obtained through UCPH BSc
course Topology) and commutative algebra (e.g., obtained through
UCPH MSc course Commutative Algebra).
Academic qualifications equivalent to a BSc degree is
recommended.
- ECTS
- 7,5 ECTS
- Type of assessment
-
Continuous assessment
- Type of assessment details
- Seven weekly homework assignments of which the five highest scores count towards the final grade, weighted equally at 10% each, and a three-hour closed-book final in-class problem set, accounting for 50% of the grade
- Aid
- Only certain aids allowed (see description below)
Weekly homework:
All aids except generative artificial intelligence are allowed for the weekly homework.Three-hour final in-class problem set:
No books, notes, or electronic aids are allowed for the three-hour final in-class problem set, apart from one personally created handwritten one-sided A4 page of notes. - Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
- Re-exam
-
30 minutes oral examination with no aids or preparation time. The oral examination will cover the entire material of the course, including the exercise sets.
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
- 36
- Preparation
- 134
- Exercises
- 36
- 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
- Emanuel Reinecke (8-786b6f746b69716b4673677a6e34717b346a71)
- Carles Checa Nualart (3-73737e507d7184783e7b853e747b)
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Kursusinformation for indskrevne studerende