Let be the -dimensional projective space over a field , whose points are the equivalence classes of -tuples ; the (co)domains of usual open charts in the sense of manifolds, which are Zariski-open subsets for general , have .
The hyperplane line bundle on is a line bundle given by the transition functions on . Its dual bundle is the tautological bundle (or universal bundle) usually denoted by and the tensor powers are , for . The total space of the tautological line bundle can be identified with and the projection is exactly , i.e. the fiber over is the line . The canonical line bundle equals .
The bundles are holomorphic if . The sheaves of (regular or holomorphic) sections are also denoted as and are said to be the twists of the structure sheaf ; they restrict to the equally denoted sheaves on any projective subvariety and these restrictions up to an isomorphism do not depend on a particular embedding into a particular projective space.