Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
|
| gptkbp:category |
Category of affine varieties
|
| gptkbp:coordinateRing |
Ring of regular functions
Finitely generated reduced k-algebra |
| gptkbp:definedIn |
Algebraically closed field
Polynomial equations |
| gptkbp:dimensions |
Non-negative integer
|
| gptkbp:example |
gptkb:Affine_plane
Algebraic curve Algebraic surface Affine line |
| gptkbp:field |
gptkb:Algebraic_geometry
|
| gptkbp:functor |
Spec functor
|
| gptkbp:hasSubgroup |
gptkb:Affine_space
|
| https://www.w3.org/2000/01/rdf-schema#label |
Affine variety
|
| gptkbp:morphism |
Regular map
|
| gptkbp:property |
gptkb:Zariski_topology
Can be irreducible or reducible Can be singular or nonsingular Closed under intersection Noetherian topological space Not necessarily closed under union Reduced scheme Irreducible if cannot be written as union of two proper subvarieties |
| gptkbp:relatedTo |
gptkb:Projective_variety
|
| gptkbp:studiedBy |
Algebraic geometers
|
| gptkbp:bfsParent |
gptkb:algebraic_geometry
|
| gptkbp:bfsLayer |
5
|