Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:geometry
gptkb:mathematical_concept |
| gptkbp:automorphismGroup |
gptkb:projective_linear_group_PGL(n+1)
|
| gptkbp:built |
set of lines through origin in (n+1)-dimensional vector space
|
| gptkbp:compact |
yes (over complex numbers)
|
| gptkbp:definedIn |
gptkb:Field
|
| gptkbp:dimensions |
n
|
| gptkbp:elements_called |
points
|
| gptkbp:example |
gptkb:projective_line_P^1
|
| 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
P^n |
| gptkbp:relatedTo |
gptkb:Euclidean_space
gptkb:Plücker_embedding gptkb:Segre_embedding gptkb:Veronese_embedding hyperplane projective variety flag variety incidence geometry complex projective space projective bundle finite projective space homogeneous polynomial projective closure projective completion projective coordinate system projective duality projective frame projective map projective metric projective subspace projective transformation real projective space |
| gptkbp:second_example |
gptkb:projective_plane_P^2
|
| gptkbp:topological_dimension |
n
|
| gptkbp:used_in |
gptkb:algebraic_geometry
gptkb:geometry computer vision differential geometry number theory physics representation theory intersection theory complex geometry moduli theory |
| gptkbp:bfsParent |
gptkb:Veronese_embedding
|
| gptkbp:bfsLayer |
6
|