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 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 2022	SS 2021	WS 2020/1	WS 2018/9	SS 2013	WS 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 workload	Contact hours	Credits (ECTS)
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 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

SS 2022 WS 2016/7 WS 2015/6 WS 2013/4

Type	SWS	Title	Lecturer(s)	Dates	Links
VO	4	Algebraic Geometry [MA5107]	Liedtke, C. Stadlmayr, C.	Mon, 10:15–11:45, MI 03.10.011 Wed, 10:15–11:45, MI 03.10.011
UE	2	Algebraic Geometry (Exercise Session) [MA5107]	Liedtke, C. Stadlmayr, C.	dates in groups

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 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.

Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Title
Time	Location	Info	Registration
Algebraic Geometry
Tue, 2022-10-11, 15:00 till 16:30	1050		till 2022-09-26 (cancelation of registration till 2022-10-04)