complex Grassmannian

GPTKB entity

Statements (29)
Predicate Object
gptkbp:instanceOf gptkb:algebraic_geometry
gptkb:mathematical_concept
Kähler manifold
homogeneous space
gptkbp:appearsIn gptkb:moduli_problems
gptkb:quantum_cohomology
enumerative geometry
gptkbp:can_be_realized_as quotient space U(n)/(U(k) × U(n-k))
gptkbp:compact true
gptkbp:connectedTo true
gptkbp:definedIn space of all k-dimensional linear subspaces of complex n-dimensional space
gptkbp:dimensions k(n-k)
gptkbp:generalizes complex projective space
gptkbp:has_cell_decomposition gptkb:Schubert_cells
gptkbp:has_cohomology_ring generated by Schubert classes
gptkbp:has_Plücker_embedding into projective space
gptkbp:hasSpecialCase Gr(1, n; C) is complex projective space CP^{n-1}
https://www.w3.org/2000/01/rdf-schema#label complex Grassmannian
gptkbp:is_homogeneous_space_for gptkb:unitary_group_U(n)
gptkbp:notation Gr(k, n; C)
gptkbp:relatedTo flag variety
real Grassmannian
gptkbp:structure Kähler manifold
projective variety
gptkbp:used_in gptkb:algebraic_geometry
differential geometry
representation theory
gptkbp:bfsParent gptkb:Hermitian_symmetric_space
gptkbp:bfsLayer 8