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| {{Distinguish|Cayley's ruled cubic surface}}
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| [[File:CayleyCubic.png|thumb|right|Real points of the Cayley surface]] | |
| In [[algebraic geometry]], the '''Cayley surface''',named after [[Arthur Cayley]], is a [[cubic surface]] in 3-dimensional [[projective space]] with four conical points. It can be given by the equation
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| :<math> wxy+ xyz+ yzw+zwx =0\ </math>
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| when the four singular points are those with three vanishing coordinates.
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| Changing variables gives several other simple equations defining the Cayley surface.
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| ==References==
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| *{{Citation | last1=Cayley | first1=Arthur | author1-link=Arthur Cayley | title=A Memoir on Cubic Surfaces | publisher=The Royal Society | year=1869 | journal=[[Philosophical Transactions of the Royal Society of London]] | issn=0080-4614 | volume=159 | pages=231–326 | jstor=108997}}
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| *{{Citation | last1=Heath-Brown | first1=D. R. | title=Proceedings of the Session in Analytic Number Theory and Diophantine Equations | publisher=Univ. Bonn | location=Bonn | series=Bonner Math. Schriften | year=2003 | volume=360 | chapter=The density of rational points on Cayley's cubic surface | pages=33 | mr=2075628}}
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| *{{Citation | last1=Hunt | first1=Bruce | title=Nice modular varieties | url=http://projecteuclid.org/getRecord?id=euclid.em/1045759526 | year=2000 | journal=Experimental Mathematics | issn=1058-6458 | volume=9 | issue=4 | pages=613–622 | mr=R1806296}}
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| ==External links==
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| *{{citation|url=http://enriques.mathematik.uni-mainz.de/docs/Ecayley.shtml|title=The Cayley cubic|first=Stephan |last=Endraß|year=2003}}
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| *[http://www.mathcurve.com/surfaces/cayley/cayley.shtml Surface de Cayley]
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| *{{mathworld|urlname=CayleyCubic|title=Cayley cubic}}
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| [[Category:Algebraic surfaces]]
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| [[Category:Complex surfaces]]
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Revision as of 13:32, 11 February 2014
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