Algorithmic Algebraic Geometry

Date and Time

Wednesday, 14:45 - 16:15, BA 9912
Start: 11.10.2000

Maple worksheets for the first course:

algsets.mws (to execute this worksheet, you need to install the casa package)

affine.mws

projective.mws

Exercises

Goal of the Lecture

The goal of the lecture is to teach how methods from the abstract machinery of algebraic geometry can be applied to solve algebraic problems.

Prerequisites

The lecture assumes familiarity with the contents of the lecture "Commutative Algebra and Algebraic Geometry", given in SS 2000 by Franz Winkler. This prerequisite may be substituted by the reading of the first chapter of Shafarevich's book cited below.

The computer algebra system Maple is used throughout the lecture. For a participant, it is required to have access to Maple version V.1 or higher.

Contents

The following list is still preliminary and is subject to change.

1. Affine Varieties
2. Normalization
3. Projective Varieties
4. Germs of Varieties
5. Riemann-Roch Theory for Curves
6. Algebraic Correspondences
7. Specialization and Generalization

Literature

1. T. Becker and V. Weispfenning. Gröbner bases - a computational approach to commutative algebra. Graduate Texts in Mathematics. Springer, 1993.
2. D. Eisenbud. Commutative Algebra with a View towards Algebraic Geometry. Springer, 1994.
3. P. Griffiths and J. Harris. Principles of algebraic geometry. John Wiley, 1978.
4. J. Harris. Algebraic geometry. Springer, 1995.
5. R. Hartshorne. Algebraic Geometry. Springer-Verlag, 1977.
6. J. M. Ruiz. The basic theory of power series. Vieweg, 1993.
7. I. R. Shafarevich. Basic algebraic geometry I. Springer, 1994.