New examples of finite \(\widetilde C_ 2\)-geometries (Q1801628)

The author constructs examples of finite \(\tilde C_ 2\)-geometries with parameters \(q+1,q-1,q+1\), where \(q\) is a power of 2. His construction starts with two hyperovals \({\mathcal O}\), \({\mathcal O}^*\) in a projective plane \(PG(2,q)\). The generalized quadrangles \(T^*_ 2({\mathcal O}^*)\) and \(T^*_ 2({\mathcal O})^{\text{dual}}\) appear as residues of the \(\tilde C_ 2\)-geometries. See also \textit{H. Van Maldeghem} [Mitt. Math. Semin. Giessen 189, 159 p. (1989; Zbl 0664.51004) and Geom. Dedicata 35, No. 1-3, 77-87 (1990; Zbl 0715.51003)].