Holomorphic Functions and Abelian Varieties
(dt. Holomorphe Funktionen und Abelsche Varietäten)
|Level, degree of commitment in original study programme||Advanced module, compulsory elective module|
|Forms of teaching and learning,
|Lecture (4 SWS), recitation class (2 SWS), |
270 hours (90 h attendance, 180 h private study)
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
|German,The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Mathematics.|
|Original study programme||M.Sc. Mathematik / Vertiefungsbereich Mathematik|
|One semester, |
Im Wechsel mit anderen advanced moduleen
|Person in charge of the module's outline||Prof. Dr. Thomas Bauer|
Holomorphic functions: Deepening knowledge about the theory of holomorphic functions of one variable (Theorem of Mittag-Leffler, Weierstraßsch product theorem, elliptic functions)
Analytic functions of several variables: Holomorphic functions, Weierstraß preparation theorem, algebraic properties of the ring of power series
Abelian varieties: Complex tori and Abelian varieties, theta functions, divisors, Néron-Severi group, Riemann-Roch theorem, projective embeddings
The students shall
- learn classical results of the advanced function theory of one variable,
- learn to deal with holomorphic functions in several variables required in complex and algebraic geometry,
- get to know Abelian varieties as an important class of complex manifolds,
- understand the study of divisors on these manifolds as an essential tool for understanding geometry and possible projective embeddings,
- be introduced to current research questions,
- practice mathematical working methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof techniques),
- improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.
None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, either Complex Analysis and Vector Analysis or Complex Analysis.
- Fischer/Lieb: Funktionentheorie. Vieweg-Verlag.
- S. Lang: Introduction to Algebraic and Abelian Functions. Springer-Verlag.
This page describes a module according to the latest valid module guide in Wintersemester 2022/23. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:
- WiSe 2016/17 (no corresponding element)
- SoSe 2018 (no corresponding element)
- WiSe 2018/19
- WiSe 2019/20
- WiSe 2020/21
- SoSe 2021
- WiSe 2021/22
- WiSe 2022/23
The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.
The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.