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gptkbp:instanceOf
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gptkb:mathematical_concept
|
|
gptkbp:can_be_defined_over
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complex numbers
finite fields
real numbers
arbitrary field
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gptkbp:canBe
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gptkb:projective_variety
affine variety
singular
irreducible
nonsingular
quasi-projective variety
reducible
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|
gptkbp:definedIn
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solution set of polynomial equations
|
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gptkbp:dimensions
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gptkb:integral
|
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gptkbp:example
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gptkb:algebraic_geometry
gptkb:elliptic_curve
algebraic hypersurface
|
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gptkbp:field
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gptkb:Algebraic_geometry
|
|
gptkbp:generalizes
|
schemes
|
|
gptkbp:hasProperty
|
gptkb:genus
gptkb:university
gptkb:singularity
gptkb:dimension
irreducibility
smoothness
|
|
gptkbp:rank
|
algebraically closed field
|
|
gptkbp:relatedTo
|
gptkb:commutative_algebra
number theory
complex geometry
|
|
gptkbp:structure
|
gptkb:fundamental_group
gptkb:Zariski_topology
gptkb:family
gptkb:blowup
gptkb:Euler_characteristic
gptkb:Field
gptkb:fiber
gptkb:Betti_number
gptkb:Chow_ring
gptkb:Fano_variety
gptkb:Hilbert_scheme
gptkb:K3_surface
gptkb:Picard_group
gptkb:line_bundle
gptkb:Calabi–Yau_variety
gptkb:Grassmannian
gptkb:Chow_variety
gptkb:Jacobian_variety
gptkb:toric_variety
gptkb:moduli_space
gptkb:Segre_variety
gptkb:Veronese_variety
gptkb:Abelian_variety
gptkb:differential_form
cohomology
divisor
morphism
rational map
resolution of singularities
cycle
canonical divisor
flag variety
quotient variety
smooth variety
automorphism group
cotangent space
secant variety
tangent space
group action
Galois action
Hodge number
coordinate ring
determinantal variety
intersection number
motivic invariant
pluricanonical form
rational variety
sheaf of regular functions
singular locus
singular variety
tangent variety
unirational variety
uniruled variety
|
|
gptkbp:studied_since
|
gptkb:19th_century
|
|
gptkbp:studiedBy
|
algebraic geometers
|
|
gptkbp:used_in
|
gptkb:topology
gptkb:Hodge_theory
physics
representation theory
arithmetic geometry
birational geometry
intersection theory
singularity theory
enumerative geometry
moduli theory
motivic theory
|
|
gptkbp:bfsParent
|
gptkb:K-theory
|
|
gptkbp:bfsLayer
|
6
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Algebraic varieties
|