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arXiv · 0810.2233

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

A. Aguglia·L. Giuzzi·G. Korchmáros
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Abstract

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 $Π$ of $PG(2,q^2)$ with the following three properties: 1. points of $Π$ are those of $PG(2,q^2)$; 2. lines of $Π$ are certain lines and conics of $PG(2,q^2)$; 3. the points in $U$ form a non-classical B-M unital in $Π$. 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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A. Aguglia, L. Giuzzi, G. Korchmáros. 2009-04-21. An alternative construction of B-M and B-T unitals in Desarguesian planes. https://doi.org/10.1016/j.disc.2009.06.023

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