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gptkbp:instanceOf
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gptkb:mathematical_concept
|
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gptkbp:canBe
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Affine
Nonsingular
Projective
Singular
|
|
gptkbp:class
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gptkb:genus
Degree
Field of definition
Irreducibility
Singularities
|
|
gptkbp:definedIn
|
Algebraically closed field
Polynomial equation in two variables
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gptkbp:dimensions
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1
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gptkbp:example
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Elliptic curve
Hyperelliptic curve
Plane cubic
Rational curve
|
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gptkbp:field
|
gptkb:Algebraic_geometry
|
|
https://www.w3.org/2000/01/rdf-schema#label
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Algebraic curves
|
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gptkbp:important_theorem
|
gptkb:Abel's_theorem
gptkb:Riemann–Roch_theorem
gptkb:Bezout's_theorem
gptkb:Hasse–Weil_theorem
gptkb:Hurwitz's_theorem
|
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gptkbp:parameter
|
Elliptic functions
Rational functions
|
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gptkbp:relatedConcept
|
gptkb:algebraic_geometry
gptkb:Intersection_theory
gptkb:Jacobian_variety
Algebraic surface
Birational geometry
Divisor
Field extension
Function field of a curve
Moduli space
|
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gptkbp:relatedTo
|
gptkb:genus
gptkb:Riemann_surfaces
Function fields
|
|
gptkbp:studiedBy
|
gptkb:David_Hilbert
gptkb:Oscar_Zariski
gptkb:Alexander_Grothendieck
gptkb:Bernhard_Riemann
Classical algebraic geometry
Modern algebraic geometry
|
|
gptkbp:used_in
|
gptkb:Number_theory
Cryptography
Mathematical physics
Coding theory
|
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gptkbp:bfsParent
|
gptkb:Riemann-Roch's_theorem_in_characteristic_p
|
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gptkbp:bfsLayer
|
5
|