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gptkbp:instanceOf
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gptkb:algebraic_geometry
gptkb:mathematical_concept
gptkb:Riemannian_manifold
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gptkbp:alsoKnownAs
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gptkb:CP^1
complex projective line
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gptkbp:automorphismGroup
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gptkb:PGL(2,C)
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gptkbp:canonicalBundle
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O(-2)
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gptkbp:cohomologyGroupH1
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0
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gptkbp:cohomologyGroupH2
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C
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gptkbp:compact
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true
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gptkbp:contains
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complex plane as open subset
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gptkbp:degreeOfCanonicalBundle
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-2
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gptkbp:dimensions
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1
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gptkbp:field
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complex numbers
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gptkbp:functionField
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C(z)
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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:hasPoint
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equivalence classes of nonzero pairs (z0, z1) in C^2
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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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projective line over C
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gptkbp:isomorphicTo
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gptkb:Riemann_sphere
one-point compactification of complex plane
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gptkbp:morphismTo
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any genus 0 curve over C
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gptkbp:PicardGroup
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Z
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gptkbp:projectiveSpace
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projective space of dimension 1 over C
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gptkbp:property
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universal curve of genus 0
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gptkbp:smooth
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true
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gptkbp:topology
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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:projective_line_over_R
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gptkbp:bfsLayer
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8
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