[Cherubino] Quaderni Elettronici del Seminario di Geometria Combinatoria 1E (Febbraio 2001), 1--14
Università degli Studi di Roma "La Sapienza" - Dipartimento di Matematica

Laura BADER, Dina GHINELLI and Tim PENTTILA
On a class of flocks of the quadratic cone
(Febbraio 2001)

Abstract. In PG(3,q), with q odd, we study the special class of flocks of quadratic cones with f(t) = $\alpha$ t2k+1 and g(t)= $\beta$ tk+1, which generalises all known infinite families of monomial flocks.
We show that new infinite classes of these flocks do not exist for small k, and, in general, if they exist, there are strong restrictions on the characteristic of the field GF(q). Furthermore, we prove that they are necessarily unique for each particular odd k, while at most two classes of examples may exist for each particular even k.

AMS Subject Classification: Primary 51E20, Secondary 51A45.
Keywords: flock, spread, translation plane.

Authors:
Laura Bader
Dipartimento di Matematica e Applicazioni - Università di Napoli "Federico II"
Complesso di Monte S. Angelo - Edificio T, Via Cintia, I-80126 Napoli (Italy)
e-mail: laura.bader@dma.unina.it
Dina Ghinelli
Dipartimento di Matematica - Università di Roma "La Sapienza"
Piazzale Aldo Moro, I-00185 Roma (Italy)
e-mail: dina@mat.uniroma1.it
Tim Penttila
Department of Mathematics and Statistics - University of Western Australia
WA 6907 Australia
e-mail: penttila@maths.uwa.edu.au
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