Unitals in Finite Desarguesian Planes

Authors:
A. Cossidente;G. L. Ebert;G. Korchmáros
Affiliations:
Dipartimento di Matematica, Università della Basilicata, via N. Sauro 85, 85100 Potenza, Italy. cossidente@unibas.it;Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA. ebert@math.udel.edu;Dipartimento di Matematica, Università della Basilicata, via N. Sauro 85, 85100 Potenza, Italy.korchmaros@unibas.it
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2001

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Abstract

We show that a suitable 2-dimensional linear system of Hermitian curves of iPG(2,iq2) defines a model for the Desarguesian plane iPG(2,iq). Using this model we give the following group-theoretic characterization of the classical unitals. A unital in iPG(2,iq2) is classical if and only if it is fixed by a linear collineation group of order 6(iq + 1)2 that fixes no point or line in iPG(2,iq2).