Smooth quadric hypersurfaces
GPTKB entity
Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
surface Quaternion |
| gptkbp:automorphismGroup |
gptkb:Orthogonal_group
|
| gptkbp:definedIn |
gptkb:geometry
Non-degenerate quadratic form |
| gptkbp:dimensions |
n-1 (for quadric in n-dimensional projective space)
|
| gptkbp:example |
Smooth quadric surface in P^3
Quadric curve (conic) in P^2 |
| https://www.w3.org/2000/01/rdf-schema#label |
Smooth quadric hypersurfaces
|
| gptkbp:isomorphicTo |
Product of projective spaces (in some cases)
|
| gptkbp:property |
Degree 2 variety
Fano variety (in some cases) Homogeneous variety Rational variety (in some dimensions) Smooth (no singular points) |
| gptkbp:relatedTo |
gptkb:Grassmannians
gptkb:Projective_geometry Quadratic forms |
| gptkbp:studiedIn |
gptkb:Algebraic_geometry
|
| gptkbp:bfsParent |
gptkb:Fano_varieties
|
| gptkbp:bfsLayer |
6
|