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Algebraic Geometry: Modern Methods
(dt. Algebraische Geometrie: Moderne Methoden)

Level, degree of commitment Specialization module, depends on importing study program
Forms of teaching and learning,
workload		 Lecture (4 SWS), recitation class (2 SWS),
270 hours (120 h attendance, 150 h private study)
Credit points,
formal requirements		 9 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination (individual examination)
Language,
Grading		 English,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics.
Subject, Origin Mathematics, M.Sc. Mathematics
Duration,
frequency		 One semester,
irregular
Person in charge of the module's outline Prof. Dr. Sönke Rollenske

Contents

The course provides an introduction to modern (cohomological) methods of algebraic geometry. These will be developed systematically and illustrated with key examples.


Qualification Goals

The students

  • grasp the basic properties of affine algebraic and projective varieties,
  • understand the interplay between abstract methods and results of commutative algebra and geometric intuition.
  • have deepened mathematical working methods (development of mathematical intuition and its formal justification, abstraction, proof),
  • have improved their oral communication skills through discussion and free speech in front of an audience in the exercises.

Prerequisites

None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, either Algebra [Bachelor Module] or Algebra [Lehramt Module], Commutative Algebra (Large Specialization Module) or Commutative Algebra (Small Specialization Module) or Algebraic Geometry: Introduction. Prior knowledge of differential geometry, number theory, or topology is helpful.


Recommended Reading

  • Görtz, Ulrich; Wedhorn, Torsten Algebraic geometry I., Vieweg + Teubner, Wiesbaden, 2010.
  • Liu, Qing Algebraic geometry and arithmetic curves, Oxford University Press, Oxford, 2002.
  • Perrin, Daniel Algebraic geometry. An introduction., Universitext. Springer-Verlag London, 2008.



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2023/24. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

  • Winter 2016/17 (no corresponding element)
  • Summer 2018 (no corresponding element)
  • Winter 2018/19 (no corresponding element)
  • Winter 2019/20 (no corresponding element)
  • Winter 2020/21 (no corresponding element)
  • Summer 2021 (no corresponding element)
  • Winter 2021/22 (no corresponding element)
  • Winter 2022/23 (no corresponding element)
  • Winter 2023/24

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.