Thomas Markwig Computational Algebraic Geometry - Spring 2013


Lecture: Fr 9-10 am, Weber 201 (last week Weber 223)
Fr 3-4 pm, Weber 201 (last week Weber 223)
Office hours: Th 11 am-1 pm, Weber 133


  1. There will be an additional lecture on Monday, May 13, 9-11am in Weber 223.

  2. The course starts on Friday May 3 and ends on Friday May 17.

  3. The short course is supposed to give an introduction to algebraic geometry from a computational point of view. That is, for all concepts introduced we will explain how Singular can be used to do computations. If there is anything you are particularly interested in, please do not hesitate to ask me. I will then try to include your requests in the course.

  4. In this course I use the following open source software which can be downloaded and installed for free: If you have trouble with the installation, please let me know. I will do my best to help you.

Lecture Notes:

The course is based on lecture notes of a summer school taught in Mexico in 2010. They are available via the following link:
Lecture Notes .
The book "A Singular introduction to commutative algebra" by Gert-Martin Greuel and Gerhard Pfister is a good source for more information on computational aspects of commutative algebra and algebraic geometry using the computer algebra system Singular. It introduces the theory and the algorithms, and everything is proved there, unlike in my lecture notes.
Moreover, on the web pages of the computer algebra system Singular you will find an online documentation for Singular which explains all its features with illustrating examples.

Singular Presentations:

The full code of the Singular presentation for the lecture notes can be downloaded via the following link:
Alternatively you can download the presentations for the chapters individually:
chapter2.demo, chapter3.demo, chapter4.demo, chapter5.demo, chapter6.demo.
Universität TübingenFB MathematikArbeitsbereich AlgebraCAS SINGULAR