  We classify singularities at infinity of polynomials of degree 3 in 3
variables, $ f (x_0, x_1, x_2) = f_1 (x_0, x_1, x_2) + f_2 (x_0, x_1, x_2) +
f_3 (x_0, x_1, x_2) $, $ f_i $ homogeneous polynomial of degree $ i $, $ i =
1,2,3 $. Based on this classification, we calculate the jump in the Milnor
number of an isolated singularity at infinity, when we pass from the special
fiber to a generic fiber. As an application of the results, we investigate the
existence of global fibrations of degree 3 polynomials in $\mathbb{C}^3$ and
search for information about the topology of the fibers in each equivalence
class.
