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gptkbp:instanceOf
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gptkb:algebraic_geometry
gptkb:mathematical_concept
gptkb:Riemannian_manifold
Complex manifold
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gptkbp:alsoKnownAs
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gptkb:Riemann_sphere
Projective line over the complex numbers
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gptkbp:automorphismGroup
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Projective linear group 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
|
1
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gptkbp:canBe
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Two copies of the complex plane
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gptkbp:compact
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true
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gptkbp:containsGenus
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0
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gptkbp:degree
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1
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gptkbp:dimensions
|
1
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gptkbp:Euler_characteristic
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2
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gptkbp:field
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gptkb:Complex_numbers
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gptkbp:firstChernClass
|
2
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gptkbp:fundamentalGroup
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Trivial
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gptkbp:genus
|
0
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gptkbp:hasConnection
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true
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gptkbp:hasCoordinateChart
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z = z1/z0 except at infinity
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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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Complex projective line
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gptkbp:isAlgebraicCurve
|
true
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gptkbp:isCompactRiemannSurface
|
true
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gptkbp:isIrreducible
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true
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gptkbp:isomorphicTo
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gptkb:Riemann_sphere
2-sphere S^2
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gptkbp:isOneDimensionalComplexManifold
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true
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gptkbp:isProjectiveVariety
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true
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gptkbp:isQuotientOf
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C^2 \\ {0} by C^*
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gptkbp:isSmooth
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true
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gptkbp:notation
|
P^1(C)
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gptkbp:numberOfIssues
|
true
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gptkbp:PicardGroup
|
Z
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gptkbp:pointAtInfinity
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[1:0]
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gptkbp:pointsSystem
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Equivalence classes of nonzero pairs (z0, z1) in C^2
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gptkbp:relatedTo
|
gptkb:geometry
gptkb:Riemann_sphere
Real projective line
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gptkbp:simplyConnected
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true
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gptkbp:topologicalType
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2-sphere
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gptkbp:universalCover
|
Itself
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gptkbp:usedIn
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gptkb:Algebraic_geometry
gptkb:Projective_geometry
Complex analysis
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gptkbp:bfsParent
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gptkb:Linear_Fractional_Transformation
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gptkbp:bfsLayer
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8
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