Special birational transformations of projective spaces

Extending some results of Crauder and Katz, and Ein and Shepherd-Barron on special Cremona transformations, we study birational transformations of PrPr onto a prime Fano manifold such that the base locus X⊂PrX⊂Pr is smooth irreducible and reduced. The main results are a complete classification when X has either dimension 1 and 2, or codimension 2. Partial results are also obtained when X has dimension 3.