complex projective space CP^{n-1}

GPTKB entity

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}