Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:automorphismGroup |
gptkb:projective_linear_group_PGL(N+1,_K)
|
| gptkbp:compactification_of |
gptkb:affine_space_A^N
|
| gptkbp:consistsOf |
lines through the origin in K^{N+1}
|
| gptkbp:definedIn |
gptkb:field_K
|
| gptkbp:dimensions |
N
|
| gptkbp:example |
gptkb:projective_line_P^1
gptkb:projective_plane_P^2 |
| gptkbp:field |
gptkb:algebraic_geometry
gptkb:geometry |
| gptkbp:generalizes |
projective plane
projective line |
| gptkbp:homogeneous_coordinates |
[x_0 : x_1 : ... : x_N]
|
| https://www.w3.org/2000/01/rdf-schema#label |
projective space P^N
|
| gptkbp:notation |
P^N(K)
P^N |
| gptkbp:relatedConcept |
gptkb:Euclidean_space
Grassmannian projective variety flag variety projective bundle projective transformation |
| gptkbp:topology |
gptkb:Zariski_topology
|
| gptkbp:used_in |
gptkb:geometry
gptkb:Plücker_embedding gptkb:Segre_embedding gptkb:Veronese_embedding computer vision birational geometry classical geometry intersection theory linear systems complex geometry classification of algebraic varieties enumerative geometry moduli theory homogeneous coordinates study of perspective projective embeddings perspective drawing projective coordinates real projective geometry rational maps embedding of varieties projective dimension theorem projective duality projective morphisms projective subspaces |
| gptkbp:bfsParent |
gptkb:Veronese_embedding
|
| gptkbp:bfsLayer |
6
|