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Algebraic Geometry: Introduction
(dt. Algebraische Geometrie: Einführung)

Level, degree of commitment Advanced module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture mit recitation classen (4 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements		 6 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		 German/English,
The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Mathematics.
Duration,
frequency		 One semester,
irregular
Person in charge of the module's outline Prof. Dr. Sönke Rollenske

Contents

Algebraic Varieties: Affine and projective varieties, Hilbert's Nullstellensatz, singularities, tangent spaces, and dimension.

Morphisms of varieties: regular and rational functions and mappings, blowups and resolution of singularities

Geometric applications: Linear systems of plane curves, cubic surfaces in space.


Qualification Goals

Students

  • can apply algebraic methods to describe geometric objects (algebraic varieties),
  • understand the geometry-algebra-geometry translation process and can apply it to posed problems,
  • have experienced how geometric problems can be tackled by using abstract algebraic techniques,
  • have developed their ability to abstract,
  • have improved their oral communication skills in exercises by practicing free speech in front of an audience and in discussion.

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, Algebra.


Applicability

Module imported from B.Sc. Mathematics.

It can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • B.Sc. Business Mathematics
  • M.Sc. Business Mathematics
  • LAaG Mathematics

When studying M.Sc. Business Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.


Recommended Reading

  • Hulek, K.: Elementare Algebraische Geometrie, Vieweg
  • Shafarevich, I.R.: Basic Algebraic Geometry, Springer



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.