Abstract
We show that a suitable 2-dimensional linear system of Hermitian curves of PG(2,q 2) defines a model for the Desarguesian plane PG(2,q). Using this model we give the following group-theoretic characterization of the classical unitals. A unital in PG(2,q 2) is classical if and only if it is fixed by a linear collineation group of order 6(q + 1)2 that fixes no point or line in PG(2,q 2).
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Cossidente, A., Ebert, G. & Korchmáros, G. Unitals in Finite Desarguesian Planes. Journal of Algebraic Combinatorics 14, 119–125 (2001). https://doi.org/10.1023/A:1011981711246
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DOI: https://doi.org/10.1023/A:1011981711246