×

A note on Buekenhout-Metz unitals. (English) Zbl 0888.51009

Hirschfeld, J. W. P. (ed.) et al., Geometry, combinatorial designs and related structures. Proceedings of the first Pythagorean conference, Island of Spetses, Greece, June 1–7, 1996. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 245, 177-180 (1997).
F. Buekenhout has given [Geom. Dedicatea 5, 189-194 (1976; Zbl 0336.50014)] a construction of unitals in \(PG(2,q^2)\) using the André representation of \(PG(2,q^2)\) in the space \(PG(4,q)\) [J. André, Math. Z. 60, 156-186 (1954; Zbl 0056.38503)]. R. Metz has shown [Geom. Dedicata 8, 125-126 (1979; Zbl 0403.51007)] that this construction produces Hermitian and non-Hermitian unitals.
In this note, the author gives a geometric criterion in \(PG(4,q)\) to decide whether the unital in \(PG(2,q^2)\) is Hermitian or not.
For the entire collection see [Zbl 0871.00034].

MSC:

51E23 Spreads and packing problems in finite geometry
PDFBibTeX XMLCite