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Modul
Algebraic Geometry [M-MATH-101724]
Credits
8Recurrence
UnregelmäßigDuration
1 SemesterLanguage
Level
4Version
1Responsible
Organisation
- KIT-Fakultät für Mathematik
Part of
Bricks
Identifier | Name | LP |
---|---|---|
T-MATH-103340 | Algebraic Geometry | 8 |
Competence Certificate
The module will be completed by an oral exam of about 30 minutes.
Competence Goal
Participants are able to
- name and discuss basic concepts concerning algebraic varieties
- apply algebraic tools, in particular those from the theory of polynomial rings, to geometric questions
- explain important results from classical algebraic geometry and their application in specific examples
- start to read recent research papers from algebraic geometry and write a thesis in this area.
Prerequisites
None
Content
- Hilbert's Nullstellensatz
- affine and projective varieties
- morphisms and rational maps
- non-singular varieties
- algebraic curves
- Riemann-Roch-Theorem
Recommendation
The contents of basic courses on algebra and number theory, including basic commutative algebra, should be well-understood.
Workload
Total work load:
Attendance: 90 minutes
- lectures, problem classes an examination
Self studies: 150 hours
- follow-up and deepening of the course contents
- work on problem sheets
- literature study and internet research relating to the course contents
- Preparation of the oral exam