The largest Erdős-Ko-Rado sets of planes in finite projective and finite classical polar spaces

Erdős-Ko-Rado sets of planes in a projective or polar space are non-extendable sets of planes such that every two have a non-empty intersection. In this article we classify all Erdős-Ko-Rado sets of planes that generate at least a 6-dimensional space. For general dimension (projective space) or rank (polar space) we give a classification of the ten largest types of Erdős-Ko-Rado sets of planes. For some small cases we find a better, sometimes complete, classification.