Veronese representation of projective Hjelmslev planes over some quadratic alternative algebras

Anneleen De Schepper; Hendrik Van Maldeghem

doi:10.1007/s00025-019-1133-5

paper

Veronese representation of projective Hjelmslev planes over some quadratic alternative algebras

arXiv:2001.03395 · doi:10.1007/s00025-019-1133-5

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 $A_{2}$ and respective absolute type $A_{2}$ , $A_{5}$ and $E_{6}$ .

51 pages