Picard group (for line bundles)

GPTKB entity

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 gptkb:scheme
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	gptkb:abelian_group
gptkbp:bfsParent	gptkb:Grothendieck_group_of_vector_bundles
gptkbp:bfsLayer	8
https://www.w3.org/2000/01/rdf-schema#label	Picard group (for line bundles)