The Rational Quartic Curve in Space of Three and Four Dimensions

Abstract

IN this tract Miss Telling has presented in compact form a great deal of information, gathered from various sources, which is not available as a whole elsewhere. The tract is divided into two chapters and a short appendix. The first chapter deals with the four-dimensional curve and its projective generation, invariants and the symbolical notation for them, fundamental polarity, trisecant planes, chords, quadratic involutions, director lines and planes, (/-lines and the manifold G, the chordal J, the quartic surface K and its nodes, Segre cubic primals, and linear complexes containing the curve, or apolar to it. In the second chapter we descend to three-dimensional space, and consider quartic curves of the first and second kind, principal, quadratic, and cubic involutions; flexes, trisecants and Hessian points, the surfaces of Steiner and Veronese, and several special kinds of quartic curves. The appendix consists of a note on involutions on the four-dimensional quartic. The Rational Quartic Curve in Space of Three and Four Dimensions: being an Introduction to Rational Curves. By H. G. Telling. (Cambridge Tracts in Mathematics and Mathematical Physics, No. 34.) Pp. viii + 78. (Cambridge: At the University Press, 1936.) 5s. net.