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Algebraic Geometry

Module MA5107

This Module is offered by Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of SS 2022 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2022SS 2021WS 2020/1WS 2018/9SS 2013WS 2012/3

Basic Information

MA5107 is a semester module in English language at Master’s level which is offered irregular.

This Module is included in the following catalogues within the study programs in physics.

  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)
Total workloadContact hoursCredits (ECTS)
270 h 90 h 9 CP

Content, Learning Outcome and Preconditions


- schemes and their morphisms
- coherent sheaves
- projective, affine, reduced, and normal schemes
- differentials
- blow-ups and normalization

Learning Outcome

After successful completion of the module the students have understood a more advanced mathematical theory. They are able to apply the learned algebraic and geometric concepts and notions to basic questions in algebraic geometry.


MA1101 Linear Algebra and Discrete Structures 1,
MA1102 Linear Algebra and Discrete Structures 2 or MA0004 Linear Algebra 1 and MA0005 Linear Algebra 2 and Discrete Structures;
MA2101 Algebra or MA2010 Algebra;
MA5120 Algebra 2

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

The module consists of a series of lectures supplemented by exercise sessions. In the lectures, theoretical principles and examples are presented in a blackboard presentation. In the exercise sessions, problems which illustrate and deepen the topics of the lectures are discussed.


blackboard, tutorial sheets


Eisenbud/Harris: The Geometry of Schemes, Springer
Görtz/Wedhorn: Algebraic Geometry I, Vieweg-Teubner
Hartshorne: Algebraic Geometry, Springer

Module Exam

Description of exams and course work

The exam will be an written examination (90 minutes).
The students will be asked to reproduce and explain definitions and results from the lecture and to give illustrating examples. Further, they are asked to apply these results as well as key arguments explained in the lecture to new examples that are given in the exam.

Exam Repetition

The exam may be repeated at the end of the semester.

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