Ruled quartic surfaces, models and classification

Polo-Blanco, Irene; van der Put, Marius; Top, Jaap

Ruled quartic surfaces, models and classification

Authors

Polo-Blanco, Irene

van der Put, Marius

Top, Jaap

Description

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. A conceptual proof is presented of a result of Rohn concerning curves in $\mathbb{P}^1\times \mathbb{P}^1$ of bi-degree $(2,2)$. The string models of Series XIII (of some ruled quartic surfaces) are based on Rohn's result.
35 pages, including 3 figures