Spreads of \(T_2(\mathcal O)\), \({\alpha}\)-flocks and ovals (Q1878295)

In this nice paper the authors provide a representation of a spread of \(T_2(O)\), \(O\) an oval of PG\((2,q)\), \(q\) even in terms of a family of \(q\) ovals of PG\((2,q)\), investigating its properties. They show that to every flock of a translation oval cone in PG\((3,q)\), \(q\) even, there corresponds a spread of \(T_2(O)\), where \(O\) is an oval depending on the flock. This yields new spreads of \(T_2(O)\), for certain ovals \(O\), and also a geometrical characterization of the ovals associated with a flock of a quadratic cone.