Prof. Franz Winkler

Commutative Algebra and Algebraic Geometry

!!! The lecture on June 3 will be held as scheduled !!!

Time and room

Lecture: Tue 13:45-15:15 in P004, Fri 12:00-13:30 in T711

Exercises: Tue 15:30-16:15 in KG416

first lecture: March 11

Short Description

Algebraic geometry is an old and intensively studied area of mathematics. It is concerned with geometric objects which can be described as the zero locus of polynomial equations, i.e. algebraic curves, surfaces, and varieties in higher dimension. Nowadays such algebraic curves and surfaces are of high importance in computer aided geometric design, computer vision, cryptography, and other application areas.

The algebraic theory which allows us to compute with such algebraic varieties is the theory of polynomials or commutative algebra. Polynomial ideals, radicals, polynomial and rational functions and mappings and the like lend themselves to computational methods from computer algebra.

In this course we will examine the relation between the algebraic theory of polynomial ideals and the geometry of curves, surfaces, and algebraic varieties.

Participants are expected to be acquainted with basics in (computer) algebra.

In the exercise session (Übungen) the students will have to solve both theoretical problems and practical problems with the help of some computer algebra system.

Final Exam (Vorlesungsklausur)