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gptkbp:instanceOf
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gptkb:geometry
gptkb:mathematical_concept
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gptkbp:automorphismGroup
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gptkb:projective_linear_group_PGL(n+1)
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gptkbp:built
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set of lines through origin in (n+1)-dimensional vector space
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gptkbp:compact
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yes (over complex numbers)
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gptkbp:definedIn
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gptkb:Field
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gptkbp:dimensions
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n
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gptkbp:elements_called
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points
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gptkbp:example
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gptkb:projective_line_P^1
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gptkbp:generalizes
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gptkb:projective_plane
gptkb:projective_line
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gptkbp:homogeneous_coordinates
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[x_0:x_1:...:x_n]
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gptkbp:notation
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P^n
P^n
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gptkbp:relatedTo
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gptkb:Euclidean_space
gptkb:projective_variety
gptkb:Plücker_embedding
gptkb:Segre_embedding
gptkb:Veronese_embedding
gptkb:real_projective_space
hyperplane
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
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gptkbp:second_example
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gptkb:projective_plane_P^2
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gptkbp:topological_dimension
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n
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gptkbp:used_in
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gptkb:algebraic_geometry
gptkb:geometry
computer vision
differential geometry
number theory
physics
representation theory
intersection theory
complex geometry
moduli theory
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gptkbp:bfsParent
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gptkb:Veronese_embedding
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gptkbp:bfsLayer
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7
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https://www.w3.org/2000/01/rdf-schema#label
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projective space P^n
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