> Algorithms in Homological and Commutative Algebra - SS11

AG Algebra und Geometrie

Algorithms in Homological and Commutative Algebra - SS 2011

Next tuesday, May 17, the lecture will not take place.

Content:


Important

Dates

Overview

We study homological methods in conjunction with several concepts from commutative algebra which are central to algebraic geometry. We will introduce all concepts from a theoretical point of view and then develop algorithms to deal with the concepts computationally. The concepts will include flatness, which we will characterize in terms of Tor, in terms of syzygies, and in terms of Fitting ideals, we will discuss the relation between depth and codimension, we will explain how to compute depth via Ext and the Koszul complex, respectively, and we will treat Cohen-Macaulay rings from a computational point of view.

Credit points

You have to pass an oral exam at the end of the term in order to get credit points.

The exercise classes are not mandatory, BUT it will be hard to pass the exam if you do not attend them.

If you want to achieve an "Uebungsschein", you must attend the exercise classes and hand in your homework regularly. If you are in doubt whether or not you need an Uebungsschein, please ask your academic advisor ("Fachstudienberater" in German). In case you study mathematics, you may find him here.

Literature

  1. Gert-Martin Greuel, Gerhard Pfister: A Singular Introduction to Commutative Algebra, Springer Verlag, with contributions by Olaf Bachmann, Christoph Lossen, and Hans Schönemann, 2002, Second edition appeared in 2007.
  2. Wolfram Decker, Christoph Lossen: Computing in Algebraic Geometry - A Quick Start using Singular, Springer Verlag, 2005, ACM 16.
  3. Wolfram Decker, Frank-Olaf Schreyer: Varieties, Gröbner bases, and algebraic curves, book in preparation.
  4. Wolfram Decker, Gerhard Pfister: A First Course in Computational Algebraic Geometry, book in preparation.
  5. Cox, Little, and O'Shea: Ideals, Varieties, and Algorithms, Springer Verlag, 2007

Last change: April 04

 

Wolfram Decker and Christian Eder

 

April 04, 2011 [top]