Veronese representation of projective Hjelmslev planes over some quadratic alternative algebras

Abstract

We geometrically characterise the Veronese representations of ring projective planes over algebras which are analogues of the dual numbers, giving rise to projective Hjelmslev planes of level 2 coordinatised over quadratic alternative algebras. These planes are related to affine buildings of relative type Ã_2 and respective absolute type Ã_2, Ã_5 and Ẽ_6