Cayley's nodal cubic surface

Real points of the Cayley 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

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, ISSN 0080-4614, JSTOR 108997, doi:10.1098/rstl.1869.0010 
• 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, ISSN 1058-6458, MR R1806296, doi:10.1080/10586458.2000.10504664 

External links

• Endraß, Stephan (2003), The Cayley cubic 
• Surface de Cayley
• Weisstein, Eric Wolfgang. "Cayley cubic". MathWorld.