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Algebraic Geometry

Module MA5107

This Module is offered by TUM 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 2021

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 description is valid from SS 2018 to WS 2021/2.

Total workloadContact hoursCredits (ECTS)
180 h 60 h 6 CP

Content, Learning Outcome and Preconditions


- dimension of schemes
- products of schemes
- separated and proper morphisms
- coherent sheaves
- differentials and smoothness

Learning Outcome

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


MA5120 Algebra 2 (Commutative algebra), some first notions of algebraic geometry (the definition of locally ringed spaces and schemes). The lecture takes place twice a week in the second half of the semester, the exercise sessions start at the beginning of the semester. If you know commutative algebra but not algebraic geometry, you should come to the exercise sessions and/or the parallel seminar on algebraic geometry to acquire the necessary background in algebraic geometry.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Please keep in mind that course announcements are regularly only completed in the semester before.

VO 2 Algebraic Geometry [MA5107] Viehmann, E. Wed, 12:15–13:45, MI 02.08.011
Fri, 12:15–13:45, MI 02.08.011
UE 2 Algebraic Geometry [Exericse Session] [MA5107] Viehmann, E. Tue, 08:30–10:00, MI 02.04.011

Learning and Teaching Methods

The module consists of a series of lectures with parallel 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 oral examination (25 minutes). Students are not allowed to bring notes or other aid or resources to the exam. 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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