Geodesic
Unitals in finite Desarguesian planes
Journal of Algebraic Combinatorics, Tome 14 (2001) no. 2, pp. 119-125.

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Summary: We show that a suitable 2-dimensional linear system of Hermitian curves of $P$G$(2, q ^{2})$ defines a model for the Desarguesian plane $P$G$(2, q)$. Using this model we give the following group-theoretic characterization of the classical unitals. A unital in $P$G$(2, q ^{2})$ 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 $P$G$(2, q ^{2})$.
Keywords: unitals, Hermitian curves, Desarguesian planes, unitary groups 
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     author = {Cossidente, A. and Ebert, G.L. and Korchm\'aros, G.},
     title = {Unitals in finite {Desarguesian} planes},
     journal = {Journal of Algebraic Combinatorics},
     pages = {119--125},
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Cossidente, A.; Ebert, G.L.; Korchmáros, G. Unitals in finite Desarguesian planes. Journal of Algebraic Combinatorics, Tome 14 (2001) no. 2, pp. 119-125. http://geodesic.mathdoc.fr/item/JAC_2001__14_2_a4/