Searching for semifield flocks
In the projective space \(PG(3,q)\) let \(K\) be a quadratic cone with vertex \(v\) ; a flock \(\mathcal {F}\) of \(K\) is a set of \(q\) disjoint conics partitioning \ \(K \setminus \{ v \}\). The interest in flocks is due to their links with many geometric objects. For instance a spread (i.e. a set of skew lines) of \(PG(3,q)\) can be associated to each flock of a quadratic cone of \ \(PG(3,q)\) ; in particular the flock is called a semifield flock if the translation plane associated to the flock via its spread is a semifield plane. Unfortunately the author does not obtain new semifield flocks, but obtains a complete classification of the investigated sets of flocks.
scientific article; zbMATH DE number 1882148