algebraic geometry

GPTKB entity
AI-created image of algebraic geometry
AI-created image

Statements (285)
Predicate Object
gptkbp:instanceOf gptkb:academic
gptkb:algebraic_geometry
gptkb:mathematical_concept
gptkbp:alternativeName Algebraic_Geometry
Algebraic_variety
abelian_variety
algebraic_curve
algebraic_group
algebraic_stack
algebraic_surface
algebraic_variety
gptkbp:automorphismGroup automorphism group
gptkbp:canBe gptkb:Affine_variety
gptkb:Projective_variety
gptkb:Quasi-projective_variety
gptkbp:class gptkb:Isomorphism
Dimension
Birational equivalence
Singularity type
gptkbp:definedIn gptkb:Field
Polynomial equations
gptkbp:dimensions non-negative integer
gptkbp:example gptkb:Algebraic_torus
gptkb:Cubic_surface
surface
Elliptic curve
Grassmannian
Quadric surface
Plane curve
gptkbp:field gptkb:algebraic_geometry
gptkb:Algebraic_geometry
gptkbp:further_developed_by gptkb:André_Weil
gptkb:David_Hilbert
gptkb:Oscar_Zariski
gptkbp:generalizes gptkb:elliptic_curve
Algebraic curve
Algebraic surface
gptkbp:has_reference gptkb:Encyclopedia_of_Mathematics
gptkb:Springer_GTM_52:_Algebraic_Geometry_by_Robin_Hartshorne
gptkbp:hasConcept gptkb:Riemann–Roch_theorem
gptkb:Zariski_topology
gptkb:algebraic_geometry
gptkb:television_series
gptkb:Hodge_theory
gptkb:Bézout's_theorem
gptkb:Chow_ring
gptkb:Hilbert_scheme
gptkb:K3_surface
gptkb:Nullstellensatz
gptkb:Picard_group
gptkb:Weil_conjectures
gptkb:category_theory
gptkb:étale_cohomology
gptkb:Grothendieck's_schemes
gptkb:toric_variety
gptkb:elliptic_curve
affine variety
scheme
Grassmannian
Homological algebra
Kähler manifold
blowup
cohomology
divisor
intersection theory
moduli space
morphism
projective variety
rational map
resolution of singularities
sheaf
flag variety
motives
gptkbp:hasDual dual abelian variety
gptkbp:hasEndomorphismRing commutative ring
gptkbp:hasHomomorphism homomorphism of abelian varieties
gptkbp:hasInvariant gptkb:genus
gptkb:Betti_number
gptkb:Chow_ring
gptkb:Picard_group
gptkb:Hodge_structure
gptkb:Fundamental_group
Degree
gptkbp:hasIsogenyClass isogeny class
gptkbp:hasJacobians gptkb:Jacobian_variety
gptkbp:hasLFunction gptkb:lion
gptkbp:hasModuliSpace moduli of abelian varieties
gptkbp:hasMorphism isogeny
gptkbp:hasProperty gptkb:Singularity
Irreducibility
Dimension
gptkbp:hasSimpleComponent simple abelian variety
gptkbp:hasSubfield gptkb:tropical_geometry
real algebraic geometry
arithmetic geometry
birational geometry
complex algebraic geometry
scheme theory
singularity theory
modern algebraic geometry
moduli theory
classical algebraic geometry
gptkbp:hasSubvariety abelian subvariety
gptkbp:hasTateModule gptkb:Tate_module
gptkbp:hasTorsionPoints gptkb:group_of_people
gptkbp:hasTorsionSubgroup torsion subgroup
gptkbp:heldBy projective variety
complete algebraic variety
group variety
https://www.w3.org/2000/01/rdf-schema#label algebraic geometry
gptkbp:introduced gptkb:Bernhard_Riemann
gptkbp:namedAfter gptkb:Niels_Henrik_Abel
gptkbp:notableIdea gptkb:Zariski_topology
gptkb:television_series
gptkb:Hodge_conjecture
gptkb:Hodge_theory
gptkb:Algebraic_stack
gptkb:Bézout's_theorem
gptkb:Chow_ring
gptkb:Derived_category
gptkb:Etale_cohomology
gptkb:Fano_variety
gptkb:Geometric_invariant_theory
gptkb:Grothendieck_group
gptkb:Hilbert_scheme
gptkb:K3_surface
gptkb:Lefschetz_theorem
gptkb:Mori_theory
gptkb:Motivic_cohomology
gptkb:Nullstellensatz
gptkb:Picard_group
gptkb:Resolution_of_singularities
gptkb:Riemann-Roch_theorem
gptkb:Schubert_calculus
gptkb:Serre_duality
gptkb:Sheaf_cohomology
gptkb:Tate_conjecture
gptkb:Weil_conjectures
gptkb:Lie_group
affine variety
scheme
Abelian variety
Algebraic closure
Algebraic curve
Algebraic extension
Algebraic function field
Algebraic map
Algebraic number field
Algebraic set
Algebraic surface
Birational geometry
Elliptic curve
Flag variety
Grassmannian
Homological algebra
Kähler manifold
Minimal model program
Rational point
Toric variety
blowup
cohomology
divisor
intersection theory
moduli space
morphism
projective variety
rational map
resolution of singularities
sheaf
gptkbp:notablePerson gptkb:Shigefumi_Mori
gptkb:André_Weil
gptkb:Jean-Pierre_Serre
gptkb:Max_Noether
gptkb:Frances_Kirwan
gptkb:Harris
gptkb:Claire_Voisin
gptkb:David_Eisenbud
gptkb:Enrico_Bombieri
gptkb:Grothendieck
gptkb:Heisuke_Hironaka
gptkb:Igor_Shafarevich
gptkb:Jean-Louis_Verdier
gptkb:Joe_Harris
gptkb:Oscar_Zariski
gptkb:Phillip_Griffiths
gptkb:Robin_Hartshorne
gptkb:Shigeru_Iitaka
gptkb:William_Fulton
gptkb:Yuri_Manin
gptkb:Zariski
gptkb:Voisin
gptkb:Mumford
gptkb:Alexander_Grothendieck
gptkb:David_Mumford
gptkb:Fulton
gptkb:Pierre_Deligne
gptkb:Vladimir_Drinfeld
gptkb:János_Kollár
gptkb:Weil
gptkb:Eisenbud
gptkb:Hartshorne
gptkb:Mori
gptkb:Serre
gptkb:Griffiths
gptkb:Arakelov
gptkb:Bombieri
gptkb:Deligne
gptkb:Drinfeld
gptkb:Kollár
gptkb:Madhav_Nori
gptkb:Manin
gptkb:Mukai
gptkb:Noether
gptkb:Kirwan
gptkb:Shafarevich
Hironaka
gptkbp:polarization ample line bundle
gptkbp:relatedTo gptkb:Scheme
gptkb:Manifold
differential geometry
mathematical physics
number theory
representation theory
real algebraic geometry
Algebraic set
arithmetic geometry
birational geometry
complex algebraic geometry
homological algebra
intersection theory
moduli spaces
scheme theory
singularity theory
toric geometry
gptkbp:structure gptkb:Zariski_topology
gptkb:algebraic_geometry
gptkb:Coordinate_ring
Sheaf
Function field
gptkbp:studiedBy Classical algebraic geometry
Modern algebraic geometry
Algebraic geometers
gptkbp:studies algebraic varieties
solutions to algebraic equations
gptkbp:used_in gptkb:Number_theory
gptkb:Singularity_theory
Complex geometry
gptkbp:usedIn cryptography
number theory
arithmetic geometry
gptkbp:uses gptkb:commutative_algebra
gptkb:topology
abstract algebra
complex analysis
differential geometry
number theory
gptkbp:bfsParent gptkb:George_Lusztig
gptkb:Shigefumi_Mori
gptkb:Alexander_von_Brill
gptkb:Friedrich_Hirzebruch
gptkb:Hilbert's_Nullstellensatz
gptkb:Hilbert's_basis_theorem
gptkb:Jean-Pierre_Serre
gptkb:King
gptkb:Michael_Atiyah
gptkb:geometry
gptkb:group_of_people
gptkb:Claire_Voisin
gptkb:David_Kazhdan
gptkb:Enrico_Bombieri
gptkb:Jean-Pierre_Demailly
gptkb:Phillip_Griffiths
gptkb:Barry_Mazur
gptkb:John_Tate
gptkb:Andrei_Okounkov
gptkb:Caucher_Birkar
gptkb:Gerd_Faltings
gptkb:June_Huh
gptkb:Laurent_Lafforgue
gptkb:Ngô_Bảo_Châu
gptkb:Peter_Scholze
gptkb:Pierre_Deligne
gptkb:Vladimir_Drinfeld
gptkb:Don_Zagier
gptkbp:bfsLayer 4