Ruled quartic surfaces, models and classification

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URI: https://hdl.handle.net/10902/28573
ISSN: 0046-5755
ISSN: 1572-9168
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Autoría
Polo Blanco, IreneAutoridad Unican; Put, Marius van der; Top. Jaan
Fecha
2011
Derechos
Attribution-NonCommercial 4.0 International. The version of record of this article, first published in Geometriae Dedicata, is available online at Publisher's website: http://dx.doi.org/10.1007/s10711-010-9500-0
Publicado en
Geometriae Dedicata, 2011, 150, 151-180
Editorial
Springer Nature
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Palabras clave
Ruled surface
Quartic suface
Grassmann variety
Dual surface
Reciprocal surface
Resumen/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.
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Attribution-NonCommercial 4.0 International. The version of record of this article, first published in Geometriae Dedicata, is available online at Publisher's website: http://dx.doi.org/10.1007/s10711-010-9500-0Excepto si se señala otra cosa, la licencia del ítem se describe como Attribution-NonCommercial 4.0 International. The version of record of this article, first published in Geometriae Dedicata, is available online at Publisher's website: http://dx.doi.org/10.1007/s10711-010-9500-0