A Mathematical background to Cubic and Quartic Schilling Models

Abstract

At the end of the twentieth century plaster models of algebraic surface were constructed by the company of Schilling. Many universities have some series of these models but a rigorous mathematical background to the theory is most often not given. In this thesis a mathematical background is given for the cubic surfaces and quartic ruled surfaces on which two series of Schilling models are based, series VII and XIII. The background consists of the classification of all complex cubic surface through the number and type of singularities lying on the surface. The real cubic surfaces are classified by which of the singularities are real and the number and configuration of the lines lying on the cubic surface. The ruled cubic and quartic surfaces all have a singular curve lying on them and they are classified by the degree of this curve.