Every summer semester
10 Credit points
For information on the duration of the modul, refer to the courses of study in which the module is used.
Non-official translation of the module descriptions. Only the German version is legally binding.
Students master the basic contents and methods of Algebraic Geometry, in particular they can independently carry out complex proofs in this area requiring a high level of mathematical expertise. Students are able to define central terms of the theory (e.g. varieties, schemes, sheaves, divisors, algebraic curves) and apply them in context. They know fundamental results of the theory (e.g. Hilbert's Nullstellensatz, Riemann-Roch theorem) and can use examples to illustrate concepts and theorems,
Furthermore, the students recognise further-reaching connections to mathematical facts already acquired. They can transfer and apply the knowledge and methods they have learnt so far to deeper mathematical problem areas. Students also expand their mathematical intuition as a result of more intensive study.
In the tutorials, students develop their ability to discuss mathematical topics and thus further prepare themselves for the requirements of the Master's module, in particular for the scientific discussion within the Master's seminar presentation and the defence of their Master's thesis.
The following basic content of teaching from the field of Algebraic Geometry is compulsory:
Basic knowledge of algebra is assumed. Basic knowledge of commutative algebra, algebraic number theory, manifolds, Riemann surfaces is helpful but not necessary
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Module structure: 1 SL, 1 bPr 1
| Allocated examiner | Workload | LP2 |
|---|---|---|
|
Teaching staff of the course
Tutorials Algebraic Geometry 1
(exercise)
Regular completion of the exercises, each with a recognisable solution approach, as well as participation in the exercise groups for the module's lecture. As a rule, participation in the exercise group includes presenting solutions to exercises twice after being asked to do so as well as regular contributions to the scientific discussion in the exercise group, for example in the form of comments and questions on the proposed solutions presented. The organiser may replace some of the exercises with face-to-face exercises. |
see above |
see above
|
(electronic) written examination in presence of usually 120 minutes, oral examination in presence or remote of usually 40 minutes, A remote electronic written examination is not permitted.
| Degree programme | Profile | Recommended start 3 | Duration | Mandatory option 4 |
|---|---|---|---|---|
| Mathematical Economics / Master of Science [FsB vom 28.02.2025] | Mathematics | 1. o. 2. o. 3. | one semester | Compulsory optional subject |
| Mathematical Economics / Master of Science [FsB vom 28.02.2025] | Economics | 1. o. 2. o. 3. | one semester | Compulsory optional subject |
| Mathematics / Master of Science [FsB vom 28.02.2025] | - | 1. o. 2. o. 3. | one semester | Compulsory optional subject |
The system can perform an automatic check for completeness for this module.
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