On linear representations of near hexagons (Q1279868)

The authors discuss linear representations of near polygons in affine spaces. All linear representations of near hexagons in an affine space of order \(q\geq 3\) and dimension up to seven are classified. If the dimension of the affine space is at least eight, then it is proved that the near hexagon necessarily contains a quad of type \(T_2^*({\mathcal O})\) and that every such quad has a rosette of ovoids, the authors conjecture that no such example exists. Also the case in which all quads are grids is considered, and a complete classification is obtained in this case.