  In this note we present two equivalent definitions for the genus of a
birational map X --> Y between smooth complex projective 3-folds. The first one
is the definition introduced in 1973 by M. A. Frumkin, the second one was
recently suggested to me by S. Cantat. By focusing first on proving that these
two definitions are equivalent, one can obtain all the results of the paper of
Frumkin in a much shorter way. In particular, the genus of an automorphism of
$\mathbb{C}^3$, view as a birational self-map of the projective space, will
easily be proved to be 0.
