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gptkbp:instance_of
|
gptkb:Control
|
|
gptkbp:analyzes
|
a 3 D model
|
|
gptkbp:can_be_used_in
|
projective space
|
|
gptkbp:constructed_in
|
intersection of three quadrics
|
|
gptkbp:depicts
|
the concept of duality in algebraic geometry
|
|
gptkbp:example
|
a cubic surface in projective geometry
a non-abelian group action
|
|
gptkbp:genus
|
gptkb:3
|
|
gptkbp:has_a_degree
|
gptkb:3
|
|
gptkbp:has_a_dual_surface
|
the dual Klein surface
|
|
gptkbp:has_a_fundamental_group
|
the symmetric group S3
|
|
gptkbp:has_a_unique_property_of
|
being self-dual
|
|
gptkbp:has_applications_in
|
gptkb:string_theory
|
|
gptkbp:has_singularities
|
gptkb:none
|
|
gptkbp:has_subgroup
|
Sym(3)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
the Klein cubic surface
|
|
gptkbp:is_a_3-dimensional_object
|
gptkb:true
|
|
gptkbp:is_a_complex_manifold
|
gptkb:true
|
|
gptkbp:is_a_double_cover_of
|
the projective plane
|
|
gptkbp:is_a_member_of
|
the family of cubic surfaces
|
|
gptkbp:is_a_model_for_studying
|
the properties of algebraic varieties
|
|
gptkbp:is_a_non-orientable_surface
|
gptkb:true
|
|
gptkbp:is_a_projective_variety
|
gptkb:true
|
|
gptkbp:is_a_smooth_surface
|
gptkb:true
|
|
gptkbp:is_a_subject_of
|
mathematical physics
|
|
gptkbp:is_a_surface_that_exhibits
|
complex behavior under transformations
|
|
gptkbp:is_an_important_example_of
|
a non-orientable surface in algebraic geometry
|
|
gptkbp:is_analyzed_in
|
topological methods
|
|
gptkbp:is_associated_with
|
the concept of duality
|
|
gptkbp:is_characterized_by
|
its symmetry properties
|
|
gptkbp:is_connected_to
|
the concept of symmetry
|
|
gptkbp:is_defined_by
|
the complex numbers
|
|
gptkbp:is_often_discussed_in
|
the topology of surfaces
|
|
gptkbp:is_related_to
|
the theory of algebraic geometry
the theory of modular forms
the classification of surfaces
the theory of Riemann surfaces
|
|
gptkbp:is_represented_in
|
homogeneous coordinates
a polynomial equation
|
|
gptkbp:is_studied_for
|
geometric properties
|
|
gptkbp:is_studied_in
|
gptkb:Mathematics
geometry
|
|
gptkbp:is_used_in
|
gptkb:topology
|
|
gptkbp:key
|
the study of algebraic surfaces
|
|
gptkbp:key_feature
|
the study of algebraic topology
the classification of algebraic surfaces.
|
|
gptkbp:model
|
the study of complex surfaces
|
|
gptkbp:named_after
|
gptkb:Felix_Klein
|
|
gptkbp:surface
|
degree 3 in projective space
embedded in higher-dimensional spaces
studied using algebraic methods
|
|
gptkbp:type_of
|
Klein surface
|
|
gptkbp:bfsParent
|
gptkb:Klein's_quartic
|
|
gptkbp:bfsLayer
|
5
|