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27 lines on a cubic surface : ウィキペディア英語版
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.
==Examples==
If \mathbb^3 has homogeneous co-ordinates (), then the set of points where
: X^3 + Y^3 + Z^3 + W^3 = 0
is a cubic surface called the Fermat cubic surface.
The Clebsch surface is the set of points where
: X^3 + Y^3 + Z^3 + W^3 = (X+Y+Z+W)^3
Cayley's nodal cubic surface is the set of points where
:WXY + XYZ + YZW + ZWX =0

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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