High Quality Content by WIKIPEDIA articles! In mathematics, in particular the subfield of algebraic geometry, a rational map is a kind of partial function between algebraic varieties. This article uses the convention that varieties are irreducible.Formally, a rational map f colon V to W between two varieties is an equivalence class of pairs (fU,U) in which fU is a morphism of varieties from an open set Usubset V to W, and two such pairs (fU,U) and (fU',U') are considered equivalent if fU and fU' coincide on the intersection U cap U' (this is, in particular, vacuously true if the intersection is empty, but since V is assumed irreducible, this is impossible). The proof that this defines an equivalence relation relies on the following lemma: * If two morphisms of varieties are equal on any open set, then they are equal.

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