complex projective space CP^{n-1}
GPTKB entity
Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
gptkb:projective_variety gptkb:Kähler_manifold |
| gptkbp:automorphismGroup |
gptkb:PGL(n,C)
|
| gptkbp:cohomologyRing |
Z[x]/(x^n)
|
| gptkbp:compact |
true
|
| gptkbp:definedIn |
complex numbers
|
| gptkbp:dimensions |
n-1
|
| gptkbp:firstChernClass |
n
|
| gptkbp:fundamentalGroup |
trivial
|
| gptkbp:hasConnection |
true
|
| gptkbp:hasSpecialCase |
CP^1 is the Riemann sphere
CP^2 is the complex projective plane |
| gptkbp:homogeneousCoordinates |
[z_1:...:z_n]
|
| gptkbp:isAlgebraicGroup |
true
|
| gptkbp:isHomogeneousSpace |
true
|
| gptkbp:isKahlerManifold |
true
|
| gptkbp:isQuotientOf |
C^n \ {0} by C^*
|
| gptkbp:isSmooth |
true
|
| gptkbp:isSymplecticManifold |
true
|
| gptkbp:realDimension |
2(n-1)
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:topology complex geometry |
| gptkbp:bfsParent |
gptkb:projective_unitary_group_PU(n)
|
| gptkbp:bfsLayer |
8
|
| https://www.w3.org/2000/01/rdf-schema#label |
complex projective space CP^{n-1}
|