Special cubic Cremona transformations of P 6 and P 7

A famous result of Crauder and Katz (1989) concerns the classification of special Cremona transformations whose base locus has dimension at most two. They also proved that a special Cremona transformation with base locus of dimension three has to be one of the following: 1) a quinto-quintic transformation of P 5 ; 2) a cubo-quintic transformation of P 6 ; or 3) a quadro-quintic transformation of P 8 . Special Cremona transformations as in Case 1) have been classified by Ein and Shepherd-Barron (1989), while in our previous work (2013), we classified special quadro-quintic Cremona transformations of P 8 . Here we consider the problem of classifying special cubo-quintic Cremona transformations of P 6 , concluding the classification of special Cremona transformations whose base locus has dimension three.