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Over complex projective space, its fibre at a line $\ell \subseteq {\mathbb{C}}^{n+1}$ is $\ell$ itself. It is a holomorphic line bundle contained in the trivial bundle. Its dual is the hyperplane line bundle.

For positive $k$ take the $k$th tensor power of the hyperplane line bundle; for negative $k$ take the corresponding power of its dual; for $k=0$ take the trivial line bundle. On the complex projective line, global sections for $k\ge 0$ correspond to polynomials of degree at most $k$ and form a space of dimension $k+1$.