On finite \(C_ n\)-geometries with thick lines (Q1923495)

Let \(\Gamma\) be a residually connected finite \(C_n\)-geometry with thick lines such that any two distinct points of \(\Gamma\) are incident with at most one line. It is generally conjectured that \(\Gamma\) has to be a polar space, and this is known to be true for \(n\geq 4\). In the paper under review, the author shows that for \(n\geq 5\) the geometry \(\Gamma\) is either a polar space or flat, i.e. every point is incident with every hyperline.