Picard group (for line bundles)

GPTKB entity

Statements (28)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:application moduli spaces
algebraic curves
algebraic surfaces
study of divisors
classification of line bundles
gptkbp:category gptkb:algebraic_geometry
gptkb:topology
group theory
gptkbp:containsElement isomorphism class of a line bundle
gptkbp:defines group of isomorphism classes of line bundles on a scheme or variety
gptkbp:field gptkb:algebraic_geometry
gptkbp:generalizes class group in number theory
gptkbp:hasInvariant gptkb:algebraic_geometry
scheme
https://www.w3.org/2000/01/rdf-schema#label Picard group (for line bundles)
gptkbp:isFinite gptkb:geometry
gptkbp:namedAfter gptkb:Émile_Picard
gptkbp:notation Pic(X)
gptkbp:operator tensor product of line bundles
gptkbp:relatedTo gptkb:Brauer_group
gptkb:divisor_class_group
gptkb:Néron–Severi_group
cohomology group H^1(X, O_X^*)
gptkbp:trivialFor gptkb:Euclidean_space
gptkbp:type abelian group
gptkbp:bfsParent gptkb:Grothendieck_group_of_vector_bundles
gptkbp:bfsLayer 7