An alternative construction of B-M and B-T unitals in Desarguesian planes

Details An alternative construction of B-M and B-T unitals in Desarguesian planes An alternative construction of B-M and B-T unitals in Desarguesian planes

2008-10-13

arxiv.org/abs/0810.2233v2

Discrete Math. 310 (22): 3162-3167 (2010)

Mathematics

Algebraic Geometry

Keywords: unital, desarguesian plane 11 pages; ISSN: 0012-365X

Scientific paper

10.1016/j.disc.2009.06.023

We present a new construction of non-classical unitals from a classical unital $U$ in $PG(2,q^2)$. The resulting non-classical unitals are B-M unitals. The idea is to find a non-standard model $\Pi$ of $PG(2,q^2)$ with the following three properties: 1. points of $\Pi$ are those of $PG(2,q^2)$; 2. lines of $\Pi$ are certain lines and conics of $PG(2,q^2)$; 3. the points in $U$ form a non-classical B-M unital in $\Pi$. Our construction also works for the B-T unital, provided that conics are replaced by certain algebraic curves of higher degree.

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