Extension of a rational map from a smooth projective curve
= Extension of a rational map from a smooth projective curve
Every <rational map of projective varieties>[rational map] from a <smooth projective curve> to a <projective variety> extends uniquely to a <morphism of algebraic varieties>[morphism]. At a missing point, the <discrete valuation ring> of the curve lets one divide homogeneous coordinates by their smallest valuation, leaving regular coordinates of which at least one is a unit.