Embedding of orthogonal Buekenhout-Metz unitals in the Desarguesian plane of order q^2

Gábor Korchmáros, Alessandro Siciliano
2019 Ars Mathematica Contemporanea  
A unital, that is a 2-(q 3 + 1, q + 1, 1) block-design, is embedded in a projective plane π of order q 2 if its points are points of π and its blocks are subsets of lines of π, the point-block incidences being the same as in π. Regarding unitals U which are isomorphic, as a block-design, to the classical unital, T. Szőnyi and the authors recently proved that the natural embedding is the unique embedding of U into the Desarguesian plane of order q 2 . In this paper we extend this uniqueness
more » ... t to all unitals which are isomorphic, as block-designs, to orthogonal Buekenhout-Metz unitals.
doi:10.26493/1855-3974.1681.4ec fatcat:ys5jiqbaazfcfcmsqfr5c3qsdu