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gptkbp:instanceOf
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gptkb:algebraic_geometry
gptkb:mathematical_concept
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gptkbp:automorphismGroup
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PGL(2,K)
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gptkbp:contains
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affine line plus a point at infinity
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gptkbp:definedIn
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gptkb:Field
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gptkbp:dimensions
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1
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gptkbp:functionField
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rational functions in one variable
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gptkbp:genus
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0
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gptkbp:heldBy
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rational curve
set of lines through the origin in a two-dimensional vector space
complete curve
irreducible variety
projective space of dimension 1
smooth curve
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gptkbp:homogeneousCoordinates
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[x:y]
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https://www.w3.org/2000/01/rdf-schema#label
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projective line P^1
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gptkbp:morphismTo
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any smooth projective curve of genus 0 is isomorphic to P^1
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gptkbp:notation
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P^1
ℙ^1
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gptkbp:overComplexNumbers
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gptkb:Riemann_sphere
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gptkbp:overFiniteField
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finite projective line
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gptkbp:overRealNumbers
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real projective line
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gptkbp:pointsSystem
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equivalence classes of nonzero vectors in K^2 under scalar multiplication
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gptkbp:usedIn
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gptkb:algebraic_geometry
gptkb:geometry
complex analysis
number theory
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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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