Veronese Representation of Projective Hjelmslev Planes Over Some Quadratic Alternative Algebras

摘要

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 (A) over tilde (2) and respective absolute type (A) over tilde (2), (A) over tilde (5) and (E) over tilde (6).