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gptkbp:instanceOf
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gptkb:algebraic_geometry
gptkb:geometry
gptkb:Hermitian_symmetric_space
Kähler manifold
symmetric space
compact Riemann surface
rational curve
smooth projective variety
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gptkbp:alsoKnownAs
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gptkb:Riemann_sphere
complex projective line
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gptkbp:anticanonicalBundle
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gptkb:O(2)
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gptkbp:automorphismGroup
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gptkb:PGL(2,C)
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gptkbp:BettiNumber0
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1
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gptkbp:BettiNumber1
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0
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gptkbp:BettiNumber2
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1
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gptkbp:canBe
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two affine charts
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gptkbp:canonicalBundle
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O(-2)
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gptkbp:compact
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true
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gptkbp:complexDimension
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1
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gptkbp:degree
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1
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gptkbp:dimensions
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1
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gptkbp:Euler_characteristic
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2
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gptkbp:field
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complex numbers
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gptkbp:firstChernClass
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2
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gptkbp:fundamentalGroup
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trivial
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gptkbp:genus
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0
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gptkbp:hasAffineChart
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C
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gptkbp:hasPoint
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all lines through the origin in C^2
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gptkbp:hasPointAtInfinity
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true
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gptkbp:HodgeDiamond
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1 0 1
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gptkbp:homogeneousCoordinates
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[z0:z1]
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https://www.w3.org/2000/01/rdf-schema#label
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CP^1
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gptkbp:isFanoVariety
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true
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gptkbp:isFlagManifold
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true
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gptkbp:isHomogeneousSpace
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true
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gptkbp:isomorphicTo
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gptkb:Riemann_sphere
extended complex plane
one-point compactification of C
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gptkbp:isQuotientOf
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C^2 \\ {0} by C^*
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gptkbp:isRational
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true
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gptkbp:isUnirational
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true
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gptkbp:isUniruled
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true
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gptkbp:PicardGroup
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Z
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gptkbp:realDimension
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2
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gptkbp:simplyConnected
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true
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gptkbp:topologicallyEquivalentTo
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2-sphere
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gptkbp:usedIn
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gptkb:algebraic_geometry
gptkb:geometry
complex analysis
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gptkbp:bfsParent
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gptkb:Riemann_sphere
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gptkbp:bfsLayer
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6
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