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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 2013

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
WS 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 2012 to WS 2016/7.

270 h 90 h 9 CP

### Content, Learning Outcome and Preconditions

#### Content

- 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.

#### Preconditions

MA1101 Linear Algebra and Discrete Structures 1
MA1102 Linear Algebra and Discrete Structures 2
MA2101 Algebra
MA5120 Algebra 2

### Courses, Learning and Teaching Methods and Literature

#### 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.

#### Media

blackboard, tutorial sheets

#### Literature

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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