|
gptkbp:instanceOf
|
gptkb:mathematical_concept
|
|
gptkbp:basisFor
|
gptkb:algebraic_geometry
|
|
gptkbp:can_be_defined_over
|
complex numbers
finite fields
number fields
arbitrary fields
|
|
gptkbp:canBe
|
gptkb:K3_surface
gptkb:manga_series
gptkb:Enriques_surface
minimal
rational surface
ruled surface
singular fibers
non-minimal
isotrivial
multi-section
multiple fibers
non-isotrivial
|
|
gptkbp:class
|
gptkb:Kodaira's_classification_of_singular_fibers
|
|
gptkbp:definedIn
|
a surface equipped with a morphism to a curve such that almost all fibers are smooth curves of genus 1
|
|
gptkbp:example
|
gptkb:Lefschetz_pencil
gptkb:K3_elliptic_surface
gptkb:modular_elliptic_surface
gptkb:rational_elliptic_surface
|
|
gptkbp:fiberContent
|
gptkb:elliptic_curve
|
|
gptkbp:field
|
gptkb:algebraic_geometry
differential geometry
complex geometry
|
|
gptkbp:hasInvariant
|
gptkb:Kodaira_dimension
gptkb:j-invariant
gptkb:Euler_characteristic
gptkb:Mordell–Weil_group
gptkb:Picard_number
|
|
gptkbp:hasSpecialCase
|
gptkb:algebraic_geometry
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
elliptic surfaces
|
|
gptkbp:relatedTo
|
gptkb:Néron_model
gptkb:Mordell–Weil_lattice
gptkb:Shioda–Tate_formula
gptkb:Weierstrass_equation
gptkb:elliptic_threefold
modular forms
elliptic fibration
|
|
gptkbp:studiedBy
|
gptkb:Kodaira
|
|
gptkbp:used_in
|
gptkb:string_theory
gptkb:moduli_problems
gptkb:mirror_symmetry
arithmetic geometry
classification of algebraic surfaces
|
|
gptkbp:bfsParent
|
gptkb:Enriques–Kodaira_classification
|
|
gptkbp:bfsLayer
|
6
|