projective algebraic variety

URI: https://gptkb.org/entity/projective_algebraic_variety
GPTKB entity
Statements (24)
Predicate Object
gptkbp:instanceOf gptkb:algebraic_geometry
gptkb:mathematical_concept
gptkbp:ambientSpace gptkb:geometry
gptkbp:contrastsWith affine algebraic variety
gptkbp:definedIn gptkb:algebraic_geometry
zero locus of homogeneous polynomials in projective space
gptkbp:dimensions dimension of the variety
gptkbp:example gptkb:projective_plane
projective curve
projective hypersurface
gptkbp:generalizes projective curve
projective surface
gptkbp:hasCoordinateRing homogeneous coordinate ring
gptkbp:hasFieldOfDefinition algebraically closed field
gptkbp:hasMorphisms projective morphisms
gptkbp:hasPoint closed point in projective space
gptkbp:hasProperty closed in Zariski topology
gptkbp:hasSingularities may be singular or nonsingular
gptkbp:hasSubgroup gptkb:algebraic_geometry
gptkbp:studiedBy algebraic geometers
gptkbp:usedIn classification of algebraic varieties
gptkbp:bfsParent gptkb:Segre_variety
gptkbp:bfsLayer 8
https://www.w3.org/2000/01/rdf-schema#label projective algebraic variety