For this embed in a projective space of dimension ; now the image of is the image of the composition still denoted . It is defined as a regular map on some open dense subset . Let the set theoretical graph be ; then define the graph of the rational map as the closure of the within . This does not depend on the choice of the dense open subset and agrees with the usual graph when is regular.
Notice that not every -point in the image of a rational map is actually set theoretically in image of the underlying map of sets of -points.
A rational map is dominant if its image as a rational map is the whole of .