  Denote by $H(d_1,d_2,d_3)$ the set of all homogeneous polynomial mappings
$F=(f_1,f_2,f_3): \C^3\to\C^3$, such that $\deg f_i=d_i$. We show that if
$\gcd(d_i,d_j)\leq 2$ for $1\leq i<j\leq 3$ and $\gcd(d_1,d_2,d_3)=1$, then
there is a non-empty Zariski open subset $U\subset H(d_1,d_2,d_3)$ such that
for every mapping $F\in U$ the map germ $(F,0)$ is $\mathcal{A}$-finitely
determined. Moreover, in this case we compute the number of discrete
singularities ($0$-stable singularities) of a generic mapping
$(f_1,f_2,f_3):\C^3\to\C^3$, where $\deg f_i=d_i$.
