Geometriae Dedicata

, Volume 150, Issue 1, pp 151–180 | Cite as

Ruled quartic surfaces, models and classification

Open Access
Original 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. 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 \({\mathbb{P}^1\times \mathbb{P}^1}\) of bi-degree (2, 2). This is given here a conceptional proof.


Ruled surface Quartic suface Grassmann variety Dual surface Reciprocal surface 

Mathematics Subject Classification (2000)

14-03 01-02 14J26 14M15 14N25 32S25 



The authors thank the referee for his very useful remarks.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  • Irene Polo-Blanco
    • 1
  • Marius van der Put
    • 2
  • Jaap Top
    • 2
  1. 1.Department MatescoUniversity of CantabriaSantaderSpain
  2. 2.Department of MathematicsUniversity of GroningenGroningenThe Netherlands

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