Ovoids and Translation Planes
- 1 October 1982
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 34 (5) , 1195-1207
- https://doi.org/10.4153/cjm-1982-082-0
Abstract
An ovoid in an orthogonal vector space V of type Ω+(2n, q) or Ω(2n – 1, q) is a set Ω of qn–1 + 1 pairwise non-perpendicular singular points. Ovoids probably do not exist when n > 4 (cf. [12], [6]) and seem to be rare when n = 4. On the other hand, when n = 3 they correspond to affine translation planes of order q2, via the Klein correspondence between PG(3, q) and the Ω+(6, q) quadric.In this paper we will describe examples having n = 3 or 4. Those with n = 4 arise from PG(2, q3), AG(2, q3), or the Ree groups. Since each example with n = 4 produces at least one with n = 3, we are led to new translation planes of order q2.Keywords
This publication has 1 reference indexed in Scilit:
- Finite GeometriesPublished by Springer Nature ,1968