Algebraic Geometry
Module MA5107
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 WS 2018/9
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 description is valid from SS 2018 to WS 2021/2.
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 180 h | 60 h | 6 CP |
Content, Learning Outcome and Preconditions
Content
- dimension of schemes
- products of schemes
- separated and proper morphisms
- coherent sheaves
- differentials and smoothness
- 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.
Preconditions
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
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| 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.
Media
blackboard, tutorial sheets
Literature
Eisenbud/Harris: The Geometry of Schemes, Springer
Görtz/Wedhorn: Algebraic Geometry I, Vieweg-Teubner
Hartshorne: Algebraic Geometry, 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.