Grassmannian of lines in P^5
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
Grassmannian |
| gptkbp:automorphismGroup |
PGL(6)
|
| gptkbp:Betti_numbers |
1, 0, 1, 0, 2, 0, 2, 0, 3, 0, 2, 0, 2, 0, 1, 0, 1
|
| gptkbp:can_be_embedded_via |
gptkb:Plücker_embedding
|
| gptkbp:cohomology_ring |
generated by Schubert cycles
|
| gptkbp:connectedTo |
true
|
| gptkbp:dimensions |
8
|
| gptkbp:Fano_index |
6
|
| https://www.w3.org/2000/01/rdf-schema#label |
Grassmannian of lines in P^5
|
| gptkbp:is_Fano_variety |
true
|
| gptkbp:is_homogeneous_space_for |
SL(6)
|
| gptkbp:is_irreducible |
true
|
| gptkbp:is_projective |
true
|
| gptkbp:is_rational |
true
|
| gptkbp:is_smooth |
true
|
| gptkbp:notation |
Gr(2,6)
|
| gptkbp:parameter |
lines in projective 5-space
|
| gptkbp:Picard_group |
Z
|
| gptkbp:Plücker_embedding_target |
P^{14}
|
| gptkbp:rank |
complex numbers
|
| gptkbp:bfsParent |
gptkb:Severi_variety
|
| gptkbp:bfsLayer |
7
|