Hyperbolic Fibrations ofPG(3,q)

✍ Scribed by R.D Baker; J.M Dover; G.L Ebert; K.L Wantz

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 186 KB
• Volume: 20
• Category: Article
• ISSN: 0195-6698
• DOI: 10.1006/eujc.1998.0249

✦ Synopsis

A hyperbolic fibration is set of q -1 hyperbolic quadrics and two lines which together partition the points of PG(3, q). The classical example of a hyperbolic fibration comes from a pencil of quadrics; however, several other families are known. In this paper we construct a new family of hyperbolic fibrations for odd prime powers q.

As an application of hyperbolic fibrations, we note that they can be used to construct 2 q-1 (not necessarily inequivalent) spreads of PG(3, q) by choosing one ruling family from each of the hyperbolic quadrics in the fibration. For our new fibration we discuss some properties of the spreads obtained in the above manner.