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 quaternary cubic polynomial which is homogeneous of degree 3 (hence, cubic). Cubic surfaces are del Pezzo surfaces.
If has homogeneous co-ordinates , then the set of points where
![[X:Y:Z:W]](https://wikimedia.org/api/rest_v1/media/math/render/svg/3efa8783fb414933a19d610f28fa21a77cf056eb)
is a cubic surface called the Fermat cubic surface.
The Clebsch surface is the set of points where
Cayley's nodal cubic surface is the set of points where
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Wikipedia