Characteristic directions of a point mapping of $P_m$ into $P_n$

The notion of characteristic directions, well known for the case of point correspondences between projective spaces of the same dimension $n$ is generalized to the case of mappings $P_m$ into $P_n$, when $m\ne n$. If $m<n$ the special importance of the asymptotic directions of the image surface $V_m\subset Р_n$ is shown. These and only these directions can be regarded as characteristic ones for some mappings $P_m$ into $P_n$, having the image $V_m$. If $m>n$ some preliminary facts concerning the characteristic directions are regarded and the case $P_3\to P_2$ is discussed.