Statements (98)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:can_be_defined_over |
complex numbers
finite fields real numbers arbitrary field |
| gptkbp:canBe |
affine variety
singular projective variety irreducible nonsingular quasi-projective variety reducible |
| gptkbp:definedIn |
solution set of polynomial equations
|
| gptkbp:dimensions |
gptkb:integral
|
| gptkbp:example |
gptkb:algebraic_geometry
gptkb:elliptic_curve algebraic hypersurface |
| gptkbp:field |
gptkb:Algebraic_geometry
|
| gptkbp:generalizes |
schemes
|
| gptkbp:hasProperty |
gptkb:genus
gptkb:university irreducibility singularity dimension smoothness |
| https://www.w3.org/2000/01/rdf-schema#label |
Algebraic varieties
|
| gptkbp:rank |
algebraically closed field
|
| gptkbp:relatedTo |
gptkb:commutative_algebra
number theory complex geometry |
| gptkbp:structure |
gptkb:fundamental_group
gptkb:Zariski_topology gptkb:family gptkb:Euler_characteristic gptkb:Field gptkb:fiber gptkb:Betti_number gptkb:Chow_ring gptkb:Fano_variety gptkb:Hilbert_scheme gptkb:K3_surface gptkb:Picard_group gptkb:Calabi–Yau_variety gptkb:Chow_variety gptkb:Jacobian_variety gptkb:toric_variety gptkb:Segre_variety gptkb:Veronese_variety Abelian variety Grassmannian blowup cohomology divisor moduli space morphism rational map resolution of singularities cycle differential form canonical divisor flag variety line bundle quotient variety smooth variety automorphism group cotangent space secant variety tangent space group action Galois action Hodge number coordinate ring determinantal variety intersection number motivic invariant pluricanonical form rational variety sheaf of regular functions singular locus singular variety tangent variety unirational variety uniruled variety |
| gptkbp:studied_since |
19th century
|
| gptkbp:studiedBy |
algebraic geometers
|
| gptkbp:used_in |
gptkb:topology
gptkb:Hodge_theory physics representation theory arithmetic geometry birational geometry intersection theory singularity theory enumerative geometry moduli theory motivic theory |
| gptkbp:bfsParent |
gptkb:K-theory
|
| gptkbp:bfsLayer |
5
|