Statements (57)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:item
|
| gptkbp:analyzes |
a tessellation of the hyperbolic plane
|
| gptkbp:can_be_used_in |
projective 3-space
|
| gptkbp:genus |
gptkb:3
|
| gptkbp:has_a_degree_of |
gptkb:4
|
| gptkbp:has_a_dual_curve |
gptkb:the_Klein_cubic_surface
|
| gptkbp:has_a_symmetry_group_of_order |
168
|
| gptkbp:has_natural_feature |
hyperbolic metric
|
| gptkbp:has_subgroup |
the symmetric group S4
|
| https://www.w3.org/2000/01/rdf-schema#label |
Klein's quartic
|
| gptkbp:is_a |
gptkb:Riemann_surface
|
| gptkbp:is_a_4-fold_cover_of |
the projective line
|
| gptkbp:is_a_4-fold_covering_of |
the projective line minus 7 points
|
| gptkbp:is_a_canonical_curve |
nan
|
| gptkbp:is_a_complete_curve |
nan
|
| gptkbp:is_a_complex_algebraic_curve |
nan
|
| gptkbp:is_a_complex_manifold |
nan
|
| gptkbp:is_a_counterexample_to |
the uniformization theorem
|
| gptkbp:is_a_fundamental_example_in |
the theory of Riemann surfaces
|
| gptkbp:is_a_hyperbolic_curve |
nan
|
| gptkbp:is_a_member_of |
the family of curves of genus 3
|
| gptkbp:is_a_non-singular_curve |
nan
|
| gptkbp:is_a_projective_variety |
nan
|
| gptkbp:is_a_quotient_of |
the hyperbolic plane
|
| gptkbp:is_a_smooth_curve |
nan
|
| gptkbp:is_a_surface_that_exhibits |
gptkb:geometric_shapes
|
| gptkbp:is_associated_with |
the theory of functions of several complex variables
|
| gptkbp:is_defined_by |
the complex numbers
|
| gptkbp:is_related_to |
modular forms
the theory of modular forms the symmetry group PSL(2,7) |
| gptkbp:is_represented_in |
a degree 4 curve
a specific polynomial equation |
| gptkbp:is_studied_in |
gptkb:topology
|
| gptkbp:is_used_in |
gptkb:string_theory
the study of algebraic geometry |
| gptkbp:key |
the study of algebraic geometry
|
| gptkbp:key_feature |
the study of algebraic topology
the theory of algebraic curves the study of complex algebraic geometry |
| gptkbp:model |
the study of complex structures
the projective plane the moduli space of curves of genus 3 |
| gptkbp:named_after |
gptkb:Felix_Klein
|
| gptkbp:surface |
connections to number theory
genus 3 interesting topological properties a rich structure applications in theoretical physics studied using tools from algebraic geometry tessellated in the hyperbolic plane used to illustrate concepts in algebraic topology used to study the properties of curves. |
| gptkbp:was_involved_in |
a quartic curve
the general theory of algebraic curves |
| gptkbp:bfsParent |
gptkb:Felix_Klein
|
| gptkbp:bfsLayer |
4
|