Ruled quartic surfaces, models and classification

Details Ruled quartic surfaces, models and classification Ruled quartic surfaces, models and classification

2009-04-15

arxiv.org/abs/0904.2374v1

Mathematics

Algebraic Geometry

35 pages, including 3 figures

Scientific paper

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.

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