ABSTRACT

In this chapter, we consider structures which are essentially flocks ‘miss­ ing’ one conic; partial flocks of deficiency one. We have considered partial parallelisms of deficiency one previously. The general idea for the study of deficiency one comes about when deriving an affine plane covered by deriv­ able nets. The derived plane, by the derivation of one of these nets, now is not covered by derivable nets but a good share of its parallel classes still are connected to derivable nets although it is apparent that the remaining lines of a given derivable net are now Baer subplanes of the derived plane. If one forgets that the derived net is, in fact, derivable, it is natural to consider such planes abstractly and ask what geometric point-line geometries are as­ sociated and what is implied of such structures when the corresponding net does turn out to be derivable.