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Cayley's nodal cubic surface
In algebraic geometry, the Cayley surface, named after Arthur Cayley, is a cubic nodal surface in 3-dimensional projective space with four conical points. It can be given by the equation
\( wxy+ xyz+ yzw+zwx =0\ \)
when the four singular points are those with three vanishing coordinates. Changing variables gives several other simple equations defining the Cayley surface.
References
Cayley, Arthur (1869), "A Memoir on Cubic Surfaces", Philosophical Transactions of the Royal Society of London (The Royal Society) 159: 231–326, doi:10.1098/rstl.1869.0010, ISSN 0080-4614, JSTOR 108997
Heath-Brown, D. R. (2003), "The density of rational points on Cayley's cubic surface", Proceedings of the Session in Analytic Number Theory and Diophantine Equations, Bonner Math. Schriften 360, Bonn: Univ. Bonn, p. 33, MR 2075628
Hunt, Bruce (2000), "Nice modular varieties", Experimental Mathematics 9 (4): 613–622, doi:10.1080/10586458.2000.10504664, ISSN 1058-6458, MR R1806296
External links
Endraß, Stephan (2003), The Cayley cubic
Surface de Cayley
Weisstein, Eric W., "Cayley cubic", MathWorld.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
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