vector bundle

plural vector bundles

1. category theoryA fiber bundle for which the fiber is a vector space.

   2012, Igor Burban, Bernd Kreussler, Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations, American Mathematical Society, page 5, This solutions actually depend on the choice of a trivialisation ξ of the universal family 𝒫(n,d) of stable vector bundles of rank n and degree d.

   2 more examples

   Let E and F be two vector bundles on a compact algebraic set X.

   1995, Mauro Beltrametti, Andrew John Sommese, The Adjunction Theory of Complex Projective Varieties, Walter de Gruyter, page 8

   Definition 6.1.5 A non-zero vector bundle #92;mathcal#123;F#125; on X is said to be decomposable if it can be written as #92;mathcal#123;F#125;#95;1#92;oplus#92;mathcal#123;F#125;#95;2 with #92;mathcal#123;F#125;#95;1 and #92;mathcal#123;F#125;#95;2 non-zero vector bundles. Otherwise it is said to be indecomposable.

   2017, David J. Benson, Representations of Elementary Abelian p-Groups and Vector Bundles, Cambridge University Press, page 130