Serre's theorem on the splitting of vector bundles

URI: https://gptkb.org/entity/Serre's_theorem_on_the_splitting_of_vector_bundles
GPTKB entity
Statements (17)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:alsoKnownAs gptkb:Serre's_splitting_theorem
gptkbp:appliesTo gptkb:geometry
algebraic vector bundles
vector bundles on projective space
gptkbp:citation gptkb:Serre,_Jean-Pierre._Faisceaux_algébriques_cohérents,_Annals_of_Mathematics,_1955
gptkbp:doesNotHoldFor projective spaces of dimension greater than 1
gptkbp:field gptkb:algebraic_geometry
https://www.w3.org/2000/01/rdf-schema#label Serre's theorem on the splitting of vector bundles
gptkbp:implies All vector bundles on the projective line split as direct sums of line bundles
gptkbp:namedAfter gptkb:Jean-Pierre_Serre
gptkbp:publicationYear 1955
gptkbp:publishedIn gptkb:Annals_of_Mathematics
gptkbp:relatedTo gptkb:Grothendieck's_theorem_on_vector_bundles_on_the_projective_line
gptkbp:sentence Every algebraic vector bundle on projective space over an algebraically closed field splits as a direct sum of line bundles if and only if the projective space is of dimension 1.
gptkbp:bfsParent gptkb:Serre's_theorem
gptkbp:bfsLayer 5