CP^n
E1531305
UNEXPLORED
CP^n is the n-dimensional complex projective space, a fundamental compact Kähler manifold in complex geometry and algebraic geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| CP^n canonical | 4 |
How this entity was disambiguated
This entity first appeared as the object of triple T22328549 — 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: CP^n Context triple: [Fubini–Study form, definedOn, CP^n]
-
A.
real projective space
Real projective space is a fundamental construction in geometry and topology obtained by identifying all nonzero real vectors that differ by a nonzero scalar multiple, generalizing the real projective line and plane to higher dimensions.
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B.
Riemann sphere
The Riemann sphere is the complex plane plus a point at infinity, forming a one-dimensional complex manifold topologically equivalent to a sphere and used to study meromorphic functions and complex analysis.
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C.
real projective plane
The real projective plane is a non-orientable two-dimensional surface in projective geometry obtained by adding "points at infinity" to the Euclidean plane so that any two distinct lines intersect in exactly one point.
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D.
Fubini–Study form
The Fubini–Study form is the canonical Kähler form on complex projective space, encoding its standard Hermitian and symplectic geometry.
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E.
4-sphere S^4
The 4-sphere S⁴ is the four-dimensional analogue of the ordinary sphere, a compact, smooth, simply connected manifold that serves as a fundamental object in topology and differential geometry.
- 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: CP^n Target entity description: CP^n is the n-dimensional complex projective space, a fundamental compact Kähler manifold in complex geometry and algebraic geometry.
-
A.
real projective space
Real projective space is a fundamental construction in geometry and topology obtained by identifying all nonzero real vectors that differ by a nonzero scalar multiple, generalizing the real projective line and plane to higher dimensions.
-
B.
Riemann sphere
The Riemann sphere is the complex plane plus a point at infinity, forming a one-dimensional complex manifold topologically equivalent to a sphere and used to study meromorphic functions and complex analysis.
-
C.
real projective plane
The real projective plane is a non-orientable two-dimensional surface in projective geometry obtained by adding "points at infinity" to the Euclidean plane so that any two distinct lines intersect in exactly one point.
-
D.
Fubini–Study form
The Fubini–Study form is the canonical Kähler form on complex projective space, encoding its standard Hermitian and symplectic geometry.
-
E.
4-sphere S^4
The 4-sphere S⁴ is the four-dimensional analogue of the ordinary sphere, a compact, smooth, simply connected manifold that serves as a fundamental object in topology and differential geometry.
- F. None of above. chosen
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.