projective space (all weights 1)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:geometry
gptkbp:alsoKnownAs	ordinary projective space
gptkbp:automorphismGroup	projective linear group
gptkbp:builtBy	gptkb:Vector
gptkbp:cohomologyRing	Z[x]/(x^{n+1})
gptkbp:dimensions	n
gptkbp:example	gptkb:real_projective_plane complex projective line
gptkbp:field	complex numbers real numbers arbitrary field
gptkbp:firstChernClass	n+1
gptkbp:fundamentalGroup	trivial (for n>1, over complex numbers)
gptkbp:hasSpecialCase	gptkb:weighted_projective_space
gptkbp:homogeneousCoordinates	yes
gptkbp:homotopyType	wedge of spheres
https://www.w3.org/2000/01/rdf-schema#label	projective space (all weights 1)
gptkbp:isQuotientOf	scalar multiplication vector space minus zero vector
gptkbp:notation	P^n [CP^n
gptkbp:property	gptkb:Riemannian_manifold compact connected simply connected (for n>1, over complex numbers)
gptkbp:relatedTo	Grassmannian flag variety
gptkbp:usedIn	gptkb:algebraic_geometry gptkb:geometry complex geometry
gptkbp:bfsParent	gptkb:weighted_projective_space
gptkbp:bfsLayer	7