All line bundles on complex projective space can be obtained by the following construction.

These line bundles can also be described in the language of divisors.

The line bundles or their first characteristic class are called Chern roots.

This construction preserves the condition of being a line bundle, and more generally the rank.

If the dimension is lower than 3, one first takes a Whitney sum with a trivial line bundle.

As a topological space, is a line bundle over the hyperbolic plane.

An important special case occurs when V is a line bundle.

The projective space case is included: see tautological line bundle.

In the theory of schemes, a related notion is ample line bundle.

(Very) ample line bundles are designed to tackle this question.