Cayley's nodal cubic surface
Encyclopedia
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
when the four singular points are those with three vanishing coordinates.
Changing variables gives several other simple equations defining the Cayley surface.
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, the Cayley surface,named after Arthur Cayley
Arthur Cayley
Arthur Cayley F.R.S. was a British mathematician. He helped found the modern British school of pure mathematics....
, is a cubic surface
Cubic surface
A cubic surface is a projective variety studied in algebraic geometry. It is an algebraic surface in three-dimensional projective space defined by a single polynomial which is homogeneous of degree 3...
in 3-dimensional projective space
Projective space
In mathematics a projective space is a set of elements similar to the set P of lines through the origin of a vector space V. The cases when V=R2 or V=R3 are the projective line and the projective plane, respectively....
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.