= Principal divisor on a complex manifold
{title2=$\operatorname{div}(f)$}
The <divisor on a complex manifold> of a nonzero global <meromorphic function> records its zero and pole orders along irreducible analytic hypersurfaces. It is called principal. Its <holomorphic line bundle associated to a divisor> is trivial: choosing the same global <meromorphic function> as the local equation on every open set gives identity transition functions. In particular, two hyperplanes in <Complex projective space> have isomorphic associated bundles, since the quotient of their homogeneous linear equations is a global <meromorphic function> with their difference as divisor.
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