ABSTRACT
Since there are so many connections with flocks of quadratic cones, there are a variety of different methods of construction and hence there are competing designations for many of the infinite classes. We begin with a rough list of the infinite classes, after which, we shall add comments indicating the complexity of the situation. To add to the confusion, there are the derived flocks (the s-square and s-inverted spreads), many of which were determined after the initial discovery of the flock. Hence, we prefer to list the infinite classes in terms of their skeletons. We formulate a very rough classification of the skeletons to include ‘semifield skeletons’, where at least one member of the skeleton is a semifield flock, ‘monomial skeletons’, where at least one member of the skeleton has defining functions (t,−f(t), g(t)), where both f and g are monomials, ‘likeable skeletons’, where the conical flock spread is defined using a likeable function, ‘transitive skeletons’, where there is a transitive action on the members of the skeleton, ‘Rigid skeletons’, where at least one flock member of the skeleton admits only the identify collineation group, and the ‘Adelaide super skeleton’, containing skeletons corresponding to the Adelaide flocks and the Subiaco flocks. Finally, the ‘linear skeleton’ consisting only of the linear flock or Desarguesian conical flock spread is not listed; however, the ‘almost linear skeletons’, where at least one member of the skeleton contains a linear subset of (q−1)/2 conics, consists of precisely the Fisher skeleton. The explicit constructions and comments are directly below. We provide the conical flock spread representation or the BLT -set representation, except for the Adelaide super skeleton, which is provided directly after the statement of the theorem.
