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Complex Geometry II
(dt. Komplexe Geometrie II)

Level, degree of commitment Specialization module, depends on importing study program
Forms of teaching and learning,
workload		 Lecture (4 SWS), recitation class (2 SWS),
270 hours (120 h attendance, 150 h private study)
Credit points,
formal requirements		 9 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Oral examination (individual examination)
Language,
Grading		 English,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics.
Origin M.Sc. Mathematics
Duration,
frequency		 One semester,
Regularly alternating with other specialization modules
Person in charge of the module's outline Prof. Dr. Sönke Rollenske

Contents

Cohomology of complex vector bundles and coherent sheaves with geometric applications (e.g., Kodaira vanishing and embedding theorem).

Cohomological properties of Kählermann manifolds.


Qualification Goals

Students will

  • grasp deeper properties of complex manifolds,
  • can use cohomological methods to solve geometric problems.
  • Have deepened mathematical working methods (development of mathematical intuition and its formal justification, abstraction, proof),
  • have improved their oral communication skills through discussion and free speech in front of an audience in the exercises.

Prerequisites

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, Complex Geometry I.


Applicability

The module can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • M.Sc. Mathematics

When studying M.Sc. Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.

The module can also be used in other study programs (export module).

The module is assigned to Pure Mathematics. Further information on eligibility can be found in the description of the study area.


Recommended Reading

  • Huybrechts, Daniel, Complex Geometry: An Introduction. Universitext, Springer-Verlag, 2005.



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2023/24. 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:

  • Winter 2016/17 (no corresponding element)
  • Summer 2018 (no corresponding element)
  • Winter 2018/19 (no corresponding element)
  • Winter 2019/20 (no corresponding element)
  • Winter 2020/21 (no corresponding element)
  • Summer 2021 (no corresponding element)
  • Winter 2021/22 (no corresponding element)
  • Winter 2022/23 (no corresponding element)
  • Winter 2023/24

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.