Some surfaces containing triple curves

Abstract

The present paper is devoted to a consideration of a type of surface which appeared incidentally in some recent work and which seems worth separate notice for its own intrinsic interest. The surface in question, which lies in space of four dimensions, is one that possesses a triple curve containing pinch-points and quadruple points, and as such is a particular case of a general surface in [4] with the same projective characters. The results given here are illustrative of those contained in the papers referred to, and with few exceptions the main facts which are used in the present discussion are quoted from the same source. In the section dealing with rational surfaces some novel results are obtained in connection with the degeneration of a plane curve into two portions, one of which is counted twice.