Quadrilateral Sets and Liftings

Abstract

In this chapter we will focus on an important concept of projective geometry: quadrilateral sets. On the one hand, these configurations can be considered a generalization of harmonic points. On the other hand, they have a close relation-ship to the liftability of lower-dimensional point configurations to prescribed higher-dimensional scenarios. Their algebraic counterparts also expose highly symmetric (almost rhythmic) structures coming from the interplay of the six intersections of four lines.