ABSTRACT
In the previous chapters, we have developed the ideas of ‡ocks of quadratic cones using translation planes whose spreads in PG(3; q) are unions of reguli that share a component. Such a translation plane admits what we call a ‘regulus-inducing’elation group. It is an amazing fact that it turns out that there is another type of translation plane with a regulus-inducing homology group that produces a ‡ock of a quadratic cone, in perhaps an oblique manner. In this chapter and in the following, we shall be connecting various translation planes with ‡ocks of quadratic cones and more generally with what shall be called ‡ocks of -cones. The present chapter generally follows the author’s work in [103] but modi…ed for this text.
