On a Class of Cubic Surfaces with Curves of the Same Species

Abstract

the latter having 4 families, namely the rectilinear generators and two families of twisted cubics. In the following I have used an indirect method of obtaining other surfaces of the same kind, no direct method being obvious. The method consists in first finding translation-surfaces of a certain form that correspond to a unicursal quartic, irreducible or not, in the plane at infinity, and then transforming these to the so-called logarithmic space by means of the transformnation X log , Y= log y, Z= log z, (1)