Sections of vector bundles

The notion of functions is essential in mathematics. However, in projective geometry, there is an unfortunate lack of functions in the traditional sense. In this video, we explain this problem of paucity of functions, and then introduce sections of vector bundles as a way to alleviate this problem. We show how these generalise vector valued functions and can be used for most of the things that functions are used for in other geometries. We illustrate one important application, the (anti-)canonical embedding which is essential in algebraic geometry. In this way, we recover a new explanation as to why projective lines are isomorphic to plane conics.