- Riemann surfaces and holomorphic images,
- topological properties, fundamental groups, coverings,
- sheaves, differential forms, integration,
- cohomology and exact sequences,
- Riemann-Roch theorem and Serre duality.
Riemannian Surfaces (M, 3.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-40-26-M-6||Riemannian Surfaces||3.0 CP (90 h)|
|CP, Effort||3.0 CP = 90 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (General)|
|Area of study||[MAT-AGCA] Algebra, Geometry and Computer Algebra|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
|P||28 h||62 h||-||-||PL1||3.0||irreg.|
- About [MAT-40-26-K-6]: Title: "Riemann Surfaces"; Presence-Time: 28 h; Self-Study: 62 h
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: irregular (by arrangement)
- Examination number: 84154 ("Riemannian Surfaces")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
Upon successful completion of this module, the students are familiar with the classical theory of Riemann surfaces which has had an influence on subsequent mathematical theories, such as the ambiguous theory of functions (e.g. radical and logarithm), differential geometry or the geometry of algebraic curves. Vice versa, by a specific example which is close to intuition (the Riemann surfaces), the students have learnt to apply general concepts related to complex analysis and geometry. They are able to name and to prove the essential statements of the lecture as well as to classify and to explain the connections.
- S. Donaldson: Riemann Surfaces,
- R. Miranda: Algebraic Curves and Riemann Surfaces,
- O. Forster: Lectures on Riemann Surfaces,
- R.C. Gunning: Lectures on Riemann Surfaces.
Requirements for attendance of the module (informal)
Requirements for attendance of the module (formal)None
References to Module / Module Number [MAT-40-26-M-6]
|Course of Study||Section||Choice/Obligation|
|[MAT-88.105-SG] M.Sc. Mathematics||[Core Modules (non specialised)] Pure Mathematics||[WP] Compulsory Elective|
|[MAT-88.706-SG] M.Sc. Mathematics International||[Core Modules (non specialised)] Pure Mathematics||[WP] Compulsory Elective|
|[MAT-GM-MPOOL-5]||General Mathematics (Introductory Modules M.Sc.)|