Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
gptkb:mathematical_concept |
| gptkbp:definedIn |
gptkb:geometry
Zero locus of homogeneous polynomials |
| gptkbp:example |
gptkb:Projective_plane
Projective curve Projective hypersurface |
| gptkbp:field |
gptkb:Algebraic_geometry
|
| gptkbp:generalizes |
gptkb:Affine_variety
|
| gptkbp:hasProperty |
Can be singular or nonsingular
Closed in Zariski topology Defined over algebraically closed field Dimension defined as Krull dimension Irreducible if not union of two proper subvarieties |
| https://www.w3.org/2000/01/rdf-schema#label |
Projective variety
|
| gptkbp:relatedConcept |
gptkb:Scheme
gptkb:Quasi-projective_variety |
| gptkbp:structure |
Sheaf of regular functions
|
| gptkbp:studiedBy |
Modern algebraic geometry
Algebraic geometers |
| gptkbp:used_in |
Classification of algebraic varieties
|
| gptkbp:bfsParent |
gptkb:algebraic_geometry
|
| gptkbp:bfsLayer |
5
|