Use this tag for questions related to algebraic vector bundles, which are morphism of varieties $E \to X$ that locally (in the Zariski topology) have the structure of a projection of a direct product $k^n × X$ onto $X$ such that the gluing preserves the linear structure of the vector space.
An algebraic vector bundle is morphism of varieties E $\to$ X that locally (in the Zariski topology) has the structure of a projection of a direct product $\mathbb k^n \times$ X onto X such that the gluing preserves the linear structure of the vector space. Here, E is said to be the fiber space (bundle space), X the base, and n the rank or dimension of the bundle. Morphisms of an algebraic vector bundle are defined in the same manner as in topology.