Some surfaces containing triple curves, II

Abstract

1. A general threefold in [5] has an apparent double surface whose projection on to a [4] is a surface which contains a triple curve and which is characterised by the fact that it has no improper nodes; such surfaces have been considered in a previous paper. In the present note we consider a class of surfaces in [5] which possess triple curves and project into surfaces in [4] having improper nodes: these are the surfaces which represent the chords of a general curve of ordinary space upon a quadric primal Ω of [5]. For the representation of a line congruence of [3] by the points of a surface on Ω, reference may be made to a previous note, the results of which are used in the present work.