Ruled quartic surfaces, models and classification

Abstract

New historical aspects of the classification, by Cayley and Cremona, of ruled quartic surfaces and the relation to string models and plaster models are presented. In a 'modern' treatment of the classification of ruled quartic surfaces the classical one is corrected and completed. The string models of Series XIII of some ruled quartic surfaces (manufactured by L. Brill and by M. Schilling) are based on a result of Rohn concerning curves in P1 × P1 of bi-degree (2, 2). This is given here a conceptional proof. © 2010 The Author(s).