An Introduction to Projective Geometry and the Klein Quadric

Abstract

In this thesis, the main topic is the Klein quadric and its properties. In order to study this important geometric object, we will need to discuss the basics of projective geometry. We will see how the Klein quadric is defined by a quadratic equation in a projective space which has dimension 5. The main focus of the thesis will be to show that the Klein quadric is an important example of parameter space and in particular, it parameterizes all the lines in the projective space of dimension 3.