Generalized Cross-Ratios and Transversals

Abstract:

After introducing the standard cross-ratio, we discuss a generalization of the cross-ratio to higher-dimensional Grassmannians. As an application, we give a short proof of the following theorem in projective geometry: Any four n-plane subspaces in general position in a projective space of dimension 2n+1 over an algebraically closed field have exactly n+1 common transversals.