Themes and goals
Algebraic geometry is an active area of research with many spectacular results, not least through its applications in number theory. It is also related with the theory of complex analysis in many ways.
This course will give an introduction to algebraic geometry on the basis of your previous knowledge of algebra. Its central goal is to give you familiarity with the notions and methods of algebraic geometry, and to explain these through examples. First we will give an introduction to the theory of sheaves, which has established itself as a fundamental tool in many areas of geometry and topology. After that we will treat the theory of algebraic curves in great detail.
Target group and accreditation
This is a 4+2 course for 9 LP. It is intended for students who are interested in one of the areas of algebra, geometry and number theory. The minimal requirement is knowledge of the previous course "Elemente der Algebra". Beyond that, it would help to have some other previous knowledge from the Schwerpunkt Algebra/Zahlentheorie, like "Algebra" oder "Diophantische Gleichungen".
In the Bachelors Mathematik and Wirtschaftsmathematik this lecture cannot be taken for examination. Bachelor students can take it as a supplementary module.
In the Masters of Mathematik, Wirtschaftsmathematik and mathematische Biometrie you can take this lecture as as a Wahlpflichtmodul Reine Mathematik.
In the old arrangement, you can take this module as a Vertiefung Algebra und Zahlentheorie. In the new arrangement, it can be chosen as a Wahlmodul.
There will be an oral examination, with participation in the exercise sessions as a requirement.
We will use our own notes, as well as the book Algebraic Geometry by Robin Hartshorne (Springer, 2005).