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gptkbp:instanceOf
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gptkb:algebraic_geometry
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gptkbp:anticanonicalBundle
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Ample
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gptkbp:anticanonicalDegree
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Positive
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gptkbp:canonicalBundle
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Negative
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gptkbp:class
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Open problem in higher dimensions
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gptkbp:classificationKnownFor
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gptkb:Dimension_2_(del_Pezzo_surfaces)
gptkb:Dimension_3_(Iskovskih,_Mori,_Mukai)
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gptkbp:definedIn
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Smooth projective varieties with ample anticanonical bundle
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gptkbp:dimensions
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Can be any positive integer
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gptkbp:example
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gptkb:geometry
gptkb:Del_Pezzo_surfaces
gptkb:Smooth_quadric_hypersurfaces
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gptkbp:field
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Algebraically closed field
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gptkbp:generalizes
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gptkb:Del_Pezzo_surfaces
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https://www.w3.org/2000/01/rdf-schema#label
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Fano varieties
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gptkbp:importantFor
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Birational geometry
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gptkbp:moduliSpace
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Not irreducible in general
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gptkbp:namedAfter
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gptkb:Gino_Fano
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gptkbp:opposedBy
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Varieties of general type
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gptkbp:PicardNumber
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Finite
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gptkbp:rationalConnectedness
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Rationally connected
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gptkbp:relatedTo
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gptkb:Mori_theory
gptkb:K3_surfaces
gptkb:Calabi–Yau_varieties
gptkb:Rational_varieties
gptkb:Uniruled_varieties
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gptkbp:studiedBy
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gptkb:Gino_Fano
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gptkbp:studiedIn
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gptkb:Algebraic_geometry
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gptkbp:usedIn
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gptkb:Mirror_symmetry
Minimal model program
Classification of algebraic varieties
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gptkbp:bfsParent
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gptkb:Mori_theory
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gptkbp:bfsLayer
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5
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