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gptkbp:instanceOf
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gptkb:mathematical_concept
projective plane
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gptkbp:automorphismGroup
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PGL(3, F)
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gptkbp:BettiNumbers
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1, 0, 1 (real projective plane)
1, 0, 1, 0, 1 (complex projective plane)
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gptkbp:compact
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true (over real or complex numbers)
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gptkbp:contains
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lines
points
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gptkbp:definedIn
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gptkb:Field
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gptkbp:dimensions
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2
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gptkbp:Euler_characteristic
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1 (real projective plane)
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gptkbp:everyTwoDistinctLinesMeetAtUniquePoint
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true
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gptkbp:everyTwoDistinctPointsLieOnUniqueLine
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true
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gptkbp:finiteVersion
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gptkb:Fano_plane
finite projective plane
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gptkbp:firstChernClass
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3 (complex projective plane)
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gptkbp:fundamentalGroup
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Z/2Z (real projective plane)
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gptkbp:generalizes
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Euclidean plane
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gptkbp:hasDual
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point-line duality
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gptkbp:hasPoint
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equivalence classes of nonzero triples (x:y:z)
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gptkbp:homogeneousCoordinates
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(x:y:z)
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https://www.w3.org/2000/01/rdf-schema#label
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projective plane P^2
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gptkbp:non-orientable
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true (real projective plane)
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gptkbp:notation
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P^2
ℙ^2
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gptkbp:realization
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gptkb:complex_projective_plane
gptkb:real_projective_plane
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gptkbp:relatedTo
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gptkb:Desargues'_theorem
gptkb:Pappus's_theorem
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gptkbp:usedFor
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studying conic sections
studying cubic curves
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gptkbp:usedIn
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gptkb:algebraic_geometry
gptkb:geometry
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gptkbp:bfsParent
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gptkb:projective_space_P^N
gptkb:projective_space_P^n
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gptkbp:bfsLayer
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7
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