Semipartial geometries, arising from locally hermitian 1-systems of $W_{5}(q)$

Abstract

It is known that every 1-system of $W_{5}(q)$ is an SPG regulus and thus defines a semipartial geometry. In this paper, the semipartial geometries arising from locally hermitian 1-systems of $W_{5}(q)$, $q$ even, will be investigated. It will be shown that non-isomorphic locally hermitian 1-systems of $W_{5}(q)$ yield non-isomorphic semipartial geometries, which implies the existence of new semipartial geometries.