Cayley surface
E930419
The Cayley surface is a classical cubic ruled surface in projective three-dimensional space, studied in algebraic geometry and named after the mathematician Arthur Cayley.
Statements (32)
| Predicate | Object |
|---|---|
| instanceOf |
algebraic surface
ⓘ
cubic surface ⓘ projective variety ⓘ ruled surface ⓘ |
| ambientSpace |
P^3
ⓘ
projective 3-space ⓘ |
| contains |
a one-parameter family of lines
ⓘ
infinitely many lines ⓘ |
| degree | 3 ⓘ |
| dimension | 2 ⓘ |
| fieldOfDefinition | complex numbers ⓘ |
| hasCoordinateDescription | can be given by a cubic polynomial in homogeneous coordinates [x:y:z:w] on P^3 ⓘ |
| hasProperty |
classical surface
ⓘ
irreducible surface ⓘ non-smooth surface ⓘ projective surface ⓘ rational surface ⓘ ruled by lines ⓘ singular surface ⓘ |
| hasSingularity |
ordinary double point
ⓘ
rational double point ⓘ |
| isClassicalExampleOf |
ruled cubic surface
ⓘ
singular cubic surface ⓘ |
| isDefinedBy | homogeneous cubic equation in four variables ⓘ |
| isRelatedTo |
Fano varieties
NERFINISHED
ⓘ
birational geometry ⓘ projective geometry ⓘ |
| isUsedAs |
example in classification of algebraic surfaces
ⓘ
example in the study of cubic hypersurfaces ⓘ example in the study of ruled surfaces ⓘ |
| namedAfter | Arthur Cayley NERFINISHED ⓘ |
| studiedIn | algebraic geometry ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.