A **line bundle** is a fundamental concept in the fields of algebraic geometry and differential geometry. To understand what a line bundle is, let's break it down into the essential components: 1. **Vector Bundle**: A vector bundle is a topological construction that consists of a base space (often a manifold) and a vector space attached to each point of that base space.
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A line bundle on a scheme is a locally free sheaf of rank one. Its global sections can define a morphism to projective space when they have no common zero.