Steiner surface
E1493310
UNEXPLORED
The Steiner surface is a classical quartic algebraic surface in projective three-space, notable for being a singular model of the real projective plane studied extensively in 19th-century geometry.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Steiner surface canonical | 2 |
| Steiner’s Roman surface | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T21610206 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Steiner surface Context triple: [Jakob Steiner, notableWork, Steiner surface]
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A.
Cayley surface
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.
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B.
Fermat surface
A Fermat surface is an algebraic surface in projective space defined by a homogeneous equation where each variable appears with the same exponent, generalizing the notion of Fermat curves to higher dimensions.
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C.
Clebsch diagonal surfaces
Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
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D.
Whitney umbrella surface
The Whitney umbrella surface is a classic example in singularity theory and differential topology, illustrating a self-intersecting surface with a pinch point singularity in three-dimensional space.
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E.
Clebsch
Clebsch is a German surname most notably associated with mathematician Alfred Clebsch, known for his contributions to algebraic geometry and invariant theory.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Steiner surface Target entity description: The Steiner surface is a classical quartic algebraic surface in projective three-space, notable for being a singular model of the real projective plane studied extensively in 19th-century geometry.
-
A.
Cayley surface
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.
-
B.
Fermat surface
A Fermat surface is an algebraic surface in projective space defined by a homogeneous equation where each variable appears with the same exponent, generalizing the notion of Fermat curves to higher dimensions.
-
C.
Clebsch diagonal surfaces
Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
-
D.
Whitney umbrella surface
The Whitney umbrella surface is a classic example in singularity theory and differential topology, illustrating a self-intersecting surface with a pinch point singularity in three-dimensional space.
-
E.
Clebsch
Clebsch is a German surname most notably associated with mathematician Alfred Clebsch, known for his contributions to algebraic geometry and invariant theory.
- F. None of above. chosen
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Steiner surface