Birational morphism
= Birational morphism
A morphism between integral varieties is birational if it induces an isomorphism of their function fields, equivalently an isomorphism on suitable dense open subsets. A proper <birational morphism> to a normal variety satisfies $f_*\mathcal O_X=\mathcal O_Y$. For point blowups of smooth surfaces this identifies sections of pulled-back <line bundles> by the <projection formula for sheaves>.