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Characterizations of Buekenhout-Metz unitals

✍ Scribed by L. R. A. Casse; Christine M. O'Keefe; Tim Penttila

Book ID
104653332
Publisher
Springer
Year
1996
Tongue
English
Weight
867 KB
Volume
59
Category
Article
ISSN
0046-5755

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✦ Synopsis

We give a characterization of the Buekenhout-Metz unitals in PG(2, q2), in the cases that q is even or q = 3, in terms of the secant lines through a single point of the unital. With the addition of extra conditions, we obtain further characterizations of Buekenhout-Metz unitals in PG(2, q2), for all q. As an application, we show that the dual of a Buekenhout-Metz unital in PG(2, q2) is a Buekenhout-Metz unital.

πŸ“œ SIMILAR VOLUMES

A characterization of Buekenhout-Metz un
A characterization of Buekenhout-Metz unitals in PG(2,q2),qeven
✍ Vito Abatangelo; Bambina Larato πŸ“‚ Article πŸ“… 1996 πŸ› Springer 🌐 English βš– 392 KB

The known examples of embedded unitals (i.e. Hermifian arcs) in PG(2, qZ) are B-unitals, i.e. they can be obtained from ovoids of PG(3, q) by a method due to Buekenhout. B-unitals arising from elliptic quadrics are called BM-unitals. Recently, BM-unitals have been classified and their collineation g

Designs arising from Buekenhout-Metz uni
Designs arising from Buekenhout-Metz unitals
✍ A. Aguglia πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 113 KB

## Abstract An affine 2–(__q__^3^,__q__^2^, __q__ + 1) design is constructed from a Buekenhout‐Metz unital of the affine plane AG(2,__q__^2^), with __q__ > 2. It is also shown that such a design is isomorphic to the point‐plane design of the affine space AG(3,__q__). Β© 2003 Wiley Periodicals, Inc.