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gptkbp:instanceOf
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gptkb:algebraic_geometry
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gptkbp:automorphismGroup
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contains torus
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gptkbp:class
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fans in lattice
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gptkbp:definedIn
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action of algebraic torus
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gptkbp:describedBy
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fans
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gptkbp:example
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gptkb:geometry
gptkb:Hirzebruch_surface
gptkb:weighted_projective_space
gptkb:toric_Fano_variety
gptkb:toric_surface
smooth variety
singular variety
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gptkbp:hasApplication
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mathematical physics
representation theory
combinatorics
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gptkbp:hasChowRing
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described by fan
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gptkbp:hasCohomology
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computable via combinatorics
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gptkbp:hasCoordinateRing
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gptkb:semigroup_algebra
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gptkbp:hasDenseOpenSubset
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gptkb:algebraic_torus
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gptkbp:hasDivisorTheory
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gptkb:Cartier_divisors
gptkb:Weil_divisors
|
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gptkbp:hasHomology
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described by fan
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gptkbp:hasIntersectionTheory
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described combinatorially
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gptkbp:hasMorphism
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toric morphism
|
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gptkbp:hasPicardGroup
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described by fan
|
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gptkbp:hasProperty
|
can be compact
can be non-compact
can be smooth
often singular
can be affine
can be described combinatorially
can be projective
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|
gptkbp:hasSingularities
|
quotient singularities
|
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gptkbp:hasSpecialCase
|
varieties with group action
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gptkbp:hasToricBlowup
|
blowup along torus-invariant subvariety
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gptkbp:hasToricBundle
|
toric fiber bundle
|
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gptkbp:hasToricDegeneration
|
degeneration to toric variety
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gptkbp:hasToricResolution
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resolution of singularities
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gptkbp:hasToricSheaf
|
sheaf with torus action
|
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gptkbp:hasToricVectorBundle
|
vector bundle with torus action
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|
https://www.w3.org/2000/01/rdf-schema#label
|
toric varieties
|
|
gptkbp:introduced
|
Demazure
|
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gptkbp:relatedTo
|
gptkb:Newton_polytope
polyhedral geometry
torus embedding
lattice polytopes
|
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gptkbp:studiedIn
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gptkb:algebraic_geometry
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gptkbp:usedIn
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gptkb:string_theory
gptkb:mirror_symmetry
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gptkbp:bfsParent
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gptkb:torus_group
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gptkbp:bfsLayer
|
5
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