A rational map is a morphism on a dense open subset, considered up to agreement on a smaller dense open subset.
It is the projective-source-and-target case of a rational map of algebraic varieties.
The indeterminacy locus is the set where a rational map has no regular local representative.
A projective Cremona transformation is a birational self-map of projective space, regular on complementary dense open subsets together with its inverse.
Composition of these birational self-maps forms the Cremona group.

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