On Möbius spaces admitting automorphism groups of type II.2
The authors study Möbius spaces admitting an automorphism group of type II.2. Let \(\mathcal{O}\) denote an ovoid in the projective space \((\mathfrak{P},\mathfrak{G})\) of dimension at least \(3\), and let \((\mathcal{O},\mathfrak{K})\) denote the geometry of plane sections of \(\mathcal{O}\). Further let \(\Gamma < \text{Aut}(\mathcal{O},\mathfrak{K})\) be a subgroup of type II.2, then the set \(S=S_\Gamma\) is an \(\infty\)-maximal subspace of \((\mathcal{O},\mathfrak{K})\). The main result is the following: If \(S\) contains a hypersphere, then either the Möbius space \((\mathcal{O},\mathfrak{K})\) is miquelian, or char\,\(K = 2\) and \((\mathcal{O},\mathfrak{K})\) is of type III.2. For the case char \(K = 2\), more detailed results are provided.
scientific article; zbMATH DE number 5911449
scientific article