  Kommutative Algebra und Algebraische Geometrie
(Commutative Algebra and Algebraic Geometry)
(326.0KA lecture, 326.0UK exercises)
Sommersemester 2020
Prof. Dr. Franz Winkler
DI. Sebastian Falkensteiner

 Time / Place: Tue 14:30 -- 15:15  (VL) / HS 11 15:30 -- 17:00  (VL / UE) / HS 11 Fri 10:15 -- 11:45  (VL) / K001A Exercise classes: 10.03., 24.03., 21.04., 05.05., 26.05., 16.06. First lecture: Tue March 3

Classical algebraic geometry is the theory of algebraic curves, surfaces, and varieties in higher dimensions. Nowadays, such algebraic varieties are of high importance in computer aided geometric design, computer vision, cryptography, and other areas.

The algebraic theory which allows us to compute with such varieties is called commutative algebra. It is concerned with polynomial equations, polynomial ideals, and polynomial and rational mappings.

Participants in the course are expected to be acquainted with basics in (computer) algebra. Much of the material for this course will be taken from the book

 J.R. Sendra, F. Winkler, S. Perez-Diaz, Rational Algebraic Curves - A Computer Algebra Approach, Springer-Verlag Berlin Heidelberg, 2008 (ISBN 978-3-540-73724-7)

 Lecture Notes: 00-Title.pdf 01-Introduction.pdf 02-Elimination.pdf 03-Algebraic Sets.pdf 04-Algebraic-Geometric Correspondence.pdf 05-Projective Algebraic Sets.pdf 06-Functions on Varieties.pdf 07-Plane Curves.pdf 08-Rational Parametrization.pdf 09-Local Parametrization.pdf 10-Dimension.pdf

Exercises:

The exercise part consists of homework exercises and a project.

 Exercises-01.pdf Exercises-02.pdf Exercises-03.pdf Exercises-04.pdf Exercises-05.pdf Project: Projects.pdf

Webpage: www.risc.jku.at/education/courses/ss2020/caag/

 syllabus.pdf