SEMINAR: Groups and Combinatorics Seminar, Hendrik Van Maldeghem (Ghent Univ.) 16:00 Friday 15/09/2017 in Weatherburn LT

Speaker: Hendrik Van Maldeghem (Universiteit Gent/Ghent University) Title: Pappian unitals in Pappian projective planes Time and place: 16:00 Friday 15/09/2017 in Weatherburn LT

Abstract: We define a class of objects in pappian projective planes by a simple algebraic formula and parametrized by quadratic field extensions. These objects turn out to be ordinary hermitian curves if the extension is separable, and projections of certain quadrics otherwise. Endowed with the secant lines, we call the resulting point-block incidence structures "Pappian unitals". These have some remarkable properties such as the lack of O'Nan configurations, the admittance of translations and a nontrivial group of projectivities, and a characterization via a geometric construction using the André representation of the projective plane relative to the quadratic extension. We classify the embeddings of all Pappian unitals in arbitrary pappian projective planes, recovering and extending a recent result by Korchmáros, Cossidente and Szönyi for finite hermitian unitals.