Rational Mapping
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 ...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.
